Emergency services official Ilze Buksa said rescuers had managed to save 15 victims from the ruins and found two bodies.
Riga's deputy mayor Andris Ameriks told the BNS the disaster could have been caused by a blast, but did not elaborate.
Up to 13 emergency brigades and 17 ambulance teams were working at the site late Thursday.
Run by the Maxima retailer, the 500 square meter (598 square yards) supermarket was built in 2011.