I don't know a specific command for this, but you can always look at the time stamps on files in the filesystem. e.g. my DVD has mount point /media/cdrom0, and when I mount my Being John Malkovich DVD, the timestamp on that directory is changed to 2000-07-18 08:10. However, I don't know if that is the burn date, or something else. I should imagine it also depends on the correctness of the clocks on the system where the files were prepared / DVD was burned.
It might be better to look at the timestamp on all files and directories and choose the latest one. In my DVD the /media/cdrom0 has the oldest timestamp. The other files have timestamps between then and 10:13 on the same day. Since this is a mass-produced, pressed DVD, I doubt the fabrication of the disc took so long, so these times are probably the timestamps when the files were prepared or copied to the fabrication machine. It would be about right based on the release date of the film, but I expect you will find some with truly mad timestamps if they were prepared on machines with inaccurate clocks!