No. You can play a regular DVD in a Blu-ray player, but you cannot play a Blu-ray disc in a regular player.
"The reason that you can't play a Blu-ray Disc on a DVD player is that the discs are embedded with more video and audio information than a DVD player is designed to read.
The "pits" used to store the information on a Blu-ray disc are much smaller than a DVD, which requires a blue laser to read the information, whereas DVD players use red lasers.
Blue lasers produce a shorter wavelength light beam, which is needed to focus on the smaller pits of a Blu-ray Disc. The pits on the disc are where the video and audio information of Blu-ray Discs (as well as DVDs and CDs) is stored."