Well, no not really. Mirror's Edge is a game where you have to navigate a maze like environment to get from start to finish in a series of levels, avoiding or killing enemies with modern weapons along the way, discovering secrets if you explore, while viewing the environment from the first person perspective.  The core game matches the FPS paradigm as much as say, Wolfenstein 3D. Don't let the fact that the game emphasizes Flight over Fight, as opposed to vice versa, fool you.

The Zelda suggestion doesn't really hold water, even if Zelda 64 was first person (as originally planned) it has no level structure, non-linear quests, conversation with NPCs, bartering, and many other traits that distinctly separate it from the FPS genre.

Certainly, there are quite a few games that involve exploration on foot from a first person perspective that definitely aren't part of the FPS genre - such as the Elder Scrolls series, or Normality - but in my opinion, Mirrors Edge is definitely one.