RAW, it depends on how the creature in question got to the Ethereal Plane.
Etherealness spell or a Ghost's Etherealness ability, no.
Succubus/ Incubus/ Night Hag's Etherealness ability, Nightmare (and friends)'s Ethereal Stride ability, or Phase Spider's Ethereal Jaunt ability, yes.
Rules as Intended: not according to a tweet by Crawford.
Page 48 of the DMG referring to the Border Ethereal (aka the fun and interavtive part of the Ethereal Plane):
Normally, creatures in the Border Ethereal can't attack creatures on the overlapped plane, and vice versa. A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don't hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.
If the target got to the Ethereal Plane through an ability like the Night Hag's Etherealness, then yes. If she can be seen, she can be targeted and damaged by Magic Missile because (even if it's just for flavour) the missiles are RAW made of "magical force". The DMG explains this point saying "The exceptions (referring to trans-planar attacks and freedom of movement hampering from its previous two sentences) are certain magical effects (including anything made of magical force) and living beings." These Magic Missiles are only present on the Material Plane, but their force is present and felt through both planes.
What this means is that not only can the Night Hag be damaged by Magic Missiles from the caster, but she can also damage the caster with HER OWN Magic Missiles! Furthermore, if a fighter has the Night Hag grappled, she can use her Etherealness ability to blink into the the Ethereal Plane, but the grapple will not be broken because a living being is still hampering her movement, regardless of whether or not the fighter can see into the Ethereal Plane. And of course, by extension, an ethereal Night Hag can grapple the fighter later and exact her revenge because he is a living being. This trans-planar touching is further evidenced by the Night Hag's 'Soulmonger' flavour text and Nightmare Haunting ability (MM pg. 178).
Eldritch Blast and Spiritual Weapon, etc. are not "made of force" and so do not qualify for the exception. Just because something deals a damage type, does not necessitate that it is made of that thing (i.e. not all fire-damage sources are made of fire, some are just hot). More to the point, force damage is non-trans-planar as defended by Jeremy "Inadmissible in Rules Court" Crawford.
Where the real fun starts is with the Etherealness SPELL.
Keep in mind that specific rules ALWAYS beat general rules. The Basic Rules state that
many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins.
Because the Night Hag simply "enters the Ethereal Plane from the Material Plane, or vice versa." (MM pg. 178), she is beholden to the limitations of the general rules on page 48 of the DMG.
Etherealness the SPELL however, gets a whole bunch of fun specific rewrites!
You step into the border regions of the Ethereal Plane, in the area where it overlaps with your current plane. You remain in the Border Ethereal for the Duration or until you use your action to dismiss the spell. During this time, you can move in any direction. If you move up or down, every foot of Movement costs an extra foot. You can see and hear the plan you originated from, but everything there looks gray, and you can't see anything more than 60 feet away.
While on the Ethereal Plane, you can only affect and be affected by other creatures on that plane. Creatures that aren't on the Ethereal Plane can't perceive you and can't interact with you, unless a Special ability or magic has given them the ability to do so.
You ignore all Objects and Effects that aren't on the Ethereal Plane, allowing you to move through Objects you perceive on the plan you originated from.
When the spell ends, you immediately return to the plane you originated from in the spot you currently occupy. If you occupy the same spot as a solid object or creature when this happens, you are immediately shunted to the nearest unoccupied space that you can occupy and take force damage equal to twice the number of feet you are moved.
This spell has no effect if you cast it while you are on the Ethereal Plane or a plane that doesn't border it, such as one of the Outer Planes.
(PHB pg. 238)
The second paragraph of the spell refers to creatures explicitly. This means that the caster is not beholden to the GENERAL rule of 'not being able to pass through living things' (DMG pg. 48), because the spell's SPECIFIC rule states that the caster can only be affected by other creatures on that plane. Not only does this mean that the caster is immune to trans-planar wrestling matches, but it also means that the caster can stroll through packed markets and mosh pits unhampered. The spell's creature-specific freedom of movement is also necessitated by the fourth paragraph which requires you to be in a creature's space- something a Night Hag cannot do at all. What she can do however, is move straight up and down at normal-movement, whereas the caster can only do so at half-movement. The Night Hag also sees 30ft into the Material Plane in lo-fi blurry colour, whereas the caster will see in high-definition black and white for 60ft.
The third paragraph of the spell refers specifically to all Objects and Effects that aren't on the Ethereal Plane. As per the Basic Rules, "A spell is a discrete magical effect", and since the caster is able to ignore all Objects and Effects that aren't on the Ethereal Plane, this means that the caster is unaffected by......... Magic Missile!
This is because the spell's specific rule of ignore all Objects and Effects that aren't on the Ethereal Plane beats the DMG's general rule of magical force exceptions.
Ignoring objects and effects through Etherealness does not extend to Wall of Force, Forcecage, etc. because those spells specifically state that they block ethereal travel. They are specifically intended and written in a way that counters/ makes an answer to ethereal travel getting through walls. This was an explicit design choice to keep out Succubi, Ghosts, and nosey 13th level casters.