The PlayStation 3 can not natively play files in the MKV file format. However, the computer program PS3 Media Server is more than capable of converting an MKV file into a more appropriate format before a streaming connection is established. You just have to configure the PS3 Media Server properly to tell it to convert the file before your PS3 attempts to access it over your network connection.
Open the PS3 Media Server program on your computer. Use the icon in either the "All Programs" menu or on your desktop (whichever is applicable).
Click the "Transcoding Settings" button at the top of the screen.
Select the "Force transcode for following extensions" option. Check the box next to the "MKV" file extension listing.
Click "Save." PS3 Media Server will transcode all MKV files into an appropriate format before streaming them to the PlayStation 3.