Since PlayStation 3 doesn’t run MKV videos, it’s best to convert them in some other compatible format and there is no better tool to do that job other than MKV2VOB.
This is a free tool that will remux MKV with x.264 video and AC3 audio to a VOB file or Blu-ray/AVCHD which is playable on the PS3. Apart from playing it on PS3, you can convert MKV files for any purpose and this is the fastest tool to do it.
I’ve tried several converters to convert MKV files, but all of them took about 1 hour and 30 minutes to convert a 4GB video file. But on the other hand, MKV2VOB did the same job in 5 minutes!
You can download this converter here: Download MKV2VOB