Yes. The damage from Hunter's Mark is reduced by a Ray of Enfeeblement.
Hunter's Mark says:
Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack
This is "extra damage", and uses the same wording as that of the Rogue's Sneak Attack:
Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll.
We know that sneak attack damage is considered part of the attack's damage roll from PHB page 196:
Critical Hits: When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.
For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.
Since Sneak Attack damage is used as an example of additional damage dice being part of the same damage roll, and Hunter's Mark relies on similar wording as Sneak Attack, the damage from Hunter's Mark should also be considered part of the attack's damage roll, and should be similarly reduced by a Ray of Enfeeblement.