Yes you can.
Let's look at the requirements for using Empowered Evocation (emphasis mine):
Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard evocation spell that you cast.
So, the requirements are (1) the spell must be a Wizard evocation spell, and (2) you must cast it. Taking each in turn:
(1) Is Magic Missiles a Wizard evocation spell?
Yes. **
We can see on the official Wizard spell list that Magic Missile appears, and it is listed as an evocation spell.
(2) Are you casting a spell when using the Wand of Magic Missile?
Yes.
The Wand of Magic Missile description reads:
While holding it, you can use an action to expend 1 or more of its charges to cast the magic missile spell from it.
On a plain reading, when using the wand you cast a spell.
Since both requirements are met, you can use the Empowered Evocation class feature when using the Wand of Magic Missile.
** A short aside **
There's some debate as to how to determine when casting a spell that belongs to many class spell lists qualifies as casting a [CLASS] spell. There's some good information in this related thread, though the prevailing opinion seems to be that RAI, if a spell sits on a class' spell list, it is a [CLASS] spell. Unauthoritative but still useful Jeremy Crawford tweet:
What ultimately makes something a [class] (wiz/sorc/etc) spell? Is
having it on your spell list enough, even if you're not high enough to
cast/don't know it/don't cast via Spellcasting? I.E., can a level 1
Sorc Wild Magic Surge off of Luck Blade's wish despite not knowing it
yet?
@SymphFan, 4:12 PM - 26 Jun 2018
A class's spell list is the list of that class's spells. #DnD
@JeremyECrawford, 5:57 PM - 26 Jun 2018