High Elf simply states:
Cantrip. You know one cantrip of your choice from
the wizard spell.
While cantrips are described as:
A cantrip is a spell that can be cast at will, without
using a spell slot and without being prepared in
advance. Repeated practice has fixed the spell in the
caster’s mind and infused the caster with the magic
needed to produce the effect over and over. A cantrip’s
spell level is 0.
Initially I was led to believe the answer was no, but the description for cantrips like Shocking Grasp and Ray of Frost simply state that the "spell's damage increases by 1d8 when you reach 5th level, 11th level, and 17th level.
Given that the free cantrip is a racial feature, I have to believe that its intended to level up as it goes to retain viability against more powerful monsters later in the game.