Chances are the video bitstream in your MKV container is one that the MP4 container can handle as well, which would be MPEG-4 Part II or H.264 video. It depends on the tool you're using to rip the Blu-rays, but the codec will probably be H.264.
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In essence, you can copy the video, audio and subtitle bitstreams from the MKV to the MP4 container and play that on the PS3. For example with FFmpeg:
ffmpeg -i in.mkv -c copy out.mp4
The benefit is that this will take less than a second because it won't re-encode the video or audio. So you won't even lose quality in the process.
A combination of mkvtoolnix and MP4Box should give you similar results.
With that being said you could simply do your Blu-ray rips in MP4 in the future—unless there's something the MKV container gives you which MP4 doesn't, maybe with regard to subtitles. If your FFmpeg command fails due to an improper subtitle codec, use the following instead, which will re-encode subtitles:
ffmpeg -i in.mkv -c:a copy -c:v copy -c:s mov_text out.mp4