I find that my ATV3 will play most anything I throw at it that loads in iTunes except for 1080i in 59.97 fps. To get mkv's to load in iTunes you need to convert the container to mp4/m4v/mov.
There may be some audio issues if there is not a companion 2 channel AAC audio track in addition to the 5.1 AC3 inside the mkv, especially if you are not feeding the digital audio output to your home theater.
Basically, you need to provide more detailed information for a more definite answer...