The mall, known as Vremena Goda (The Seasons), opened in 2007 and houses over 150 stores.
"We are providing medical assistance to all the victims," Sobyanin said.
Mayor Sergei Sobyanin said some of those injured had suffered burns, and that emergency services were working on the scene.
Russian news agencies quoted investigators as saying that there had been no ammonia leak at the site as had been suspected for a time.
Video footage showed flooding throughout the building and steam flowing out of a doorway.
The mall, known as Vremena Goda (The Seasons), opened in 2007 and houses over 150 stores.
"We are providing medical assistance to all the victims," Sobyanin said.