1. MKV is a container, not a format or a codec.
2. "DVD" has specifically defined format and encoding standards. MKV containers don't meet those specs. DVD is encoded as MPEG2. MPEG2 can be encoded in MPEG containers, and/or authored for DVD disc playback as MPEG2 inside VOB containers. DVD is almost always interlaced or telecined.
-A summary of the DVD specifications for properly encoded MPEG2/DVD for PAL/NTSC/NTSC-FILM is here:
http://www.videohelp.com/dvd#tech
- A breakdown of the file structure for authored DVD video burned to DVD disc is here:
http://www.videohelp.com/dvd#struct
You can burn mkv video as-is to DVD blank media or BluRay blank disc as "data" files, then look for a player that will accept mkv files on optical disc and play them. You can also copy mkv as-is to an external media player and hope that the mkv encoding can be translated by the external player -- or burn as "data" files to USB flash drives or external hard drives, etc., and play them in players that will accept those storage media.
If you want valid "DVD" file and disc structure for burning to DVD-R or DVD+R/DL blank discs, a general workflow would be this:
1. Decode mkv video with a decoder program or editor.
2. If necessary, resize to DVD frame size standards, apply interlacing, pulldown, etc.
3. re-encode the decoded video to the proper frame size, GOP spec, bitrate, audio sampling rate, etc., as prescribed for DVD.
4. Use a free or paid authoring program to author and create the file structure for DVD disc.
5. Burn to DVD blank media.