The rescue service estimated that approximately 500 square meters (5,300 square feet) of roof collapsed, destroying large sections of the store's high walls and nearly all its front windows.
The building was completed in November 2011.
The Lithuania-owned Maxima was reportedly renting the space.
Maxima officials refused to comment and said that they would release a statement later.
The supermarket is located in a densely populated neighborhood between downtown Riga and the city's airport.
