No specific guidance is stated
There's nothing specific about the action economy of using a vial of antitoxin in the Adventuring Gear section of the basic rules (or the corresponding section of the PHB). The description merely says:
Antitoxin. A creature that drinks this vial of liquid gains advantage on saving throws against poison for 1 hour. It confers no benefit to undead or constructs.
It's not called out as magical, so it would simply involve the use of an object.
Interacting with nonmagical objects
As part of your turn, you can interact with one object for free (also known as your "free object interaction"), with any additional interactions requiring the Use an Object action:
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
If you want to interact with a second object, you need to use your action. Some magic items and other special objects always require an action to use, as stated in their descriptions.
The Use an Object action is described in more detail here:
You normally interact with an object while doing something else, such as when you draw a sword as part of an attack. When an object requires your action for its use, you take the Use an Object action. This action is also useful when you want to interact with more than one object on your turn.
Some examples of what you might use your object interaction for are given in this sidebar:
Here are a few examples of the sorts of thing you can do in tandem with your movement and action:
- withdraw a potion from your backpack
- pick up a dropped axe
- take a bauble from a table
- remove a ring from your finger
- stuff some food into your mouth
- plant a banner in the ground
- fish a few coins from your belt pouch
- drink all the ale in a flagon
As you can see, it takes an object interaction to retrieve an item you don't already have out (whether from the ground or your pack). Alternately, you can use an object interaction to consume a consumable item that you already have out.
The action economy of antitoxins
You have one free object interaction per turn; any additional interactions require the Use an Object action.
It would presumably use your free object interaction to just retrieve the antitoxin, unless you already had it out. Nothing suggests that retrieving and drinking it would be part of the same action/interaction.
Once you have taken the antitoxin out, you'd still need to take the Use an Object action to then drink it. Assuming you've already used your free object interaction to take the antitoxin vial out, you can only consume it by taking the Use an Object action as your action. (Unless you are a Thief rogue; their Fast Hands feature lets them take the Use an Object action as a bonus action.) Otherwise, you'd need to wait until your next turn and use your free object interaction to do it on that turn instead.
The same would be true of drinking any other nonmagical substance in combat (i.e. when action economy matters). You'd need to withdraw it first with one object interaction, then take the Use an Object action to consume it or wait to use your free object interaction on your next turn.
In short: 1 object interaction to take the antitoxin out, another one to consume it. Since you have only one free object interaction per turn, doing both on the same turn would require you to take the Use an Object action.