Lots of gray space
Tell the DM what you want to do
If SevenSidedDie were still answering questions, he would remind us that:
Your character can do things not covered by the actions in this chapter […] The only limits to the actions you can attempt are your imagination and your character's ability scores. (PHB, p. 193)
Just tell your DM you are trying to get by the minotaur, and it will be up to them on how to adjudicate it.
If you are looking for more rules-based structure, there are a number of possible ways to get past the minotaur, but unfortunately most of them happen in parts of the movement and space-control rules that aren't well-defined. None of them explicitly contradict RAW - they are not prohibited - but most of them require a DM to make a ruling about whether to permit something the rules don't expressly allow. I am not suggesting that they are necessarily advisable or available, only that they are possibilities, depending on how your DM rules.
Not entering the space: Vertical control
Options that rely on you not entering the space of the minotaur may mean you need to pass above it. However, vertical space in 5e is not well-defined:
Each creature takes up a different amount of space. The Size Categories table shows how much space a creature of a particular size controls in combat...
Large 10 by 10 ft.
As a Large creature, the minotaur controls a ten foot by ten foot area around it, but we are not told the volume it controls, nor how high its controlled space extends. For that matter, neither do we know how tall it is.
Cf:
How is a creature's space defined?
What are the height (and weight) size ranges for each size category of creature?
Can you fly over a Medium enemy creature in a 10ft tall corridor?
At what point do you leave a creature's reach when moving vertically?
Climb Over and Around
You have specified that the hallway is "a standard 10 ft wide". You have not specified how high it is. If the hallway is high enough, any character can approach the minotaur, climb up the wall, pass over its space, and climb down the other side (or jump down).
Each foot of movement costs 1 extra foot (2 extra feet in difficult terrain) when you’re climbing, swimming, or crawling.
Dash would give you extra movement distance if you needed it. As far as I know, any character can climb (although centaurs have penalties to do so). The walls in a 'standard' hallway are likely vertical and slick, and would thus require an ability check:
At the DM’s option, climbing a slippery vertical surface or one with few handholds requires a successful Strength (Athletics) check.
Jump over it (standing)
Assuming the hallway has enough clearance, you can jump over the minotaur without entering its space. You will need at least ten feet of horizontal jump movement, as well as enough vertical jump movement to clear whatever the DM has determined its vertical space height to be. Unfortunately, there aren't clear rules on a jump that has both horizontal and vertical components. A high jump assumes that you are moving vertically, only. A long jump assumes you are moving horizontally, but that you may need to clear vertical obstacles:
At your DM's option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump's distance), such as a hedge or low wall. Otherwise, you hit it.
A DC10 check is potentially required to clear a low obstacle, but we are not told what DC might be required to clear a high obstacle. DMs will need to make a ruling. Alternatively, we could attempt a long jump so long that the minotaur becomes a low obstacle by being no taller than a quarter of the distance jumped. This distance is likely beyond what can automatically be jumped within the normal Strength range of characters, but we can make longer jumps with an Athletics check whose DC, again, would be set by the DM:
Your Strength (Athletics) check covers difficult situations you encounter while climbing, jumping, or swimming. Examples include the following activities:...You try to jump an unusually long distance or pull off a stunt midjump.
Jump over it (prone)
If the prospect of jumping over a standing minotaur is too daunting, either because of the corridor height limit, or your difficulty in attaining the height required, you might be able to make it easier on yourself by first knocking the minotaur down. Note that no rule says that a prone creature controls less space, but your DM might rule that the prone minotaur controls less vertical space.
Make a Shove attack, and then jump over:
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you.
Grapple and then move it behind you
The grappling rules say that once you grapple a creature,
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.
While there is a size limit to who you can grapple, there is no explicit weight limit - which is good, because monster stat blocks do not typically include weight. Further, it is not clear whether the Strength-based limits on what you can lift, drag, and carry apply to creatures or just to objects. Finally, it is not clear what moving a grappled creature "with you" means - are you required to maintain the relative positions you had when the grapple was initiated, or can you move them around you? If the grappling rules says that you can "carry" them, surely you are not doing that at arm's length - you would need to move them into your space. And if you can do that, could you not then set them down in the space behind you (effectively moving them over top of you)? Real-world grappling techniques which allow you to do just that include a fallaway suplex, a koshinage (hip throw), and a sudori (disappearing throw). The first of these requires you to be strong enough to lift the minotaur with your arms, the second with your legs, and the third only that the minotaur have some forward motion toward you.
Entering their space
The rules for moving say that you can move through a nonhostile creature's space, but you can't move through the hostile minotaur's space if you are size Medium. However, the rules do not prohibit you from entering the minotaur's space, only from willingly ending your movement in its space. But what does 'ending your movement' mean - pausing it while you break up you movement and take an action, or declaring that you have no movement left or will not be using any more of your movement? If only the latter, a number of options present themselves.
Climb on, then over it
In the DMG's Climb Onto a Bigger Creature option, we are told:
If one creature wants to jump onto another creature, it can do so by grappling.
The minotaur is of a size that can be grappled by you, so you first grapple it, then climb onto it (entering its square), then let yourself down on the other side, releasing the grapple and moving away (leaving its square). Why is this permitted? Perhaps you didn't move through its space per se, rather you entered its space while it was grappled and then 'released the grapple' when you were on the other side - that is, you accomplished it through your successful grappling check rather than your movement. Or perhaps as a specific option, this supersedes the general movement rule of not moving through a hostile creature's space.
Enter its space, and then force it to leave
You can't pass through its space, and you can't enter its space and then stay there - but perhaps you can enter its space and then force it to leave, effectively switching places with it. Enter its space and then make a Shove attack, directing it toward where you were. Narratively, this can be considered something like an hijinage (elbow throw), jujinage (double elbow throw), or kaitenage (rotary throw). All of these techniques are executed by entering your opponent's space, turning yourself 180 degrees, and throwing them into or beyond the space you formerly occupied.
