I'd be comfortable with it either way, depending on how darkvision works. It seems from the way darkvision is described in the rules that it works sui generis, but if you decide that darkvision operates by perceiving photons of a normally nonvisible wavelength then you can argue that you would see any of those in the mirror as well (technically, mirrors reflect photons not "light"). Since most mirrors aren't designed to reflect these wavelengths, though, probably what you'd see would be badly garbled/unrecognizable and probably not useful in any normal sense... not being able to see nonvisible light means I'm not really sure what it might look like. The mirror might seem "shiny," or something.
So probably no.