The rules, in this case are pretty clear. The spell never mentions mirrors or reflections, it “summons illusory duplicates." Spell names aren’t indicative of their mechanical effect. See Chill Touch.
There’s also vampire wizard statblock that has Mirror Image on its spell list.
It would be funny if the spell just failed though.
Mirror image specifies that it blocks attacks that are targeted at the caster. Magic missile has no “attack” component, it automatically hits. Mirror image also ignores AoE damage. The specific wording is “A duplicate can be destroyed only by an attack that hits it. It ignores all other damage and effects.”
We just had this discussion at our table on Saturday.