Depends on ther formats your TV supports, Just do some research.
it also depends on the format the MKV contains. The TV may support the MKV container just fine, but whatever video/audio codec is inside it, the TV can not use.
Your TV may come with a software for streaming as well.
Mine came with Nero Media Home, and it streams MKV files with H264/AC3 codecs just fine, but it will not if I stream form WMP. Something similar may be happening for you.
May look into Nero Media Home. Although its a paid program, it does offer a trial to see if it works for you.
There are also some free alternatives, such as TVersity. I didn't like this one myself, but it does work.