The Tass agency quoted firefighters as saying that 40 of the missing at the Winter Cherry mall in Kemerovo are children.
Many children perished after being trapped in the cinemas on the fourth floor where staff had locked the doors to prevent people from slipping in without tickets.
News agencies said more than 100 people had been evacuated from the mall, which contains cinemas, restaurants and shops.
Anna Zarechneva, who was on the top floor where the fire started, watching a movie with her husband and son, said they only found out about the fire when a man ran into the theater shouting. A criminal investigation was begun. The shopping center opened in 2013 and also included a petting zoo, children's center and bowling.
An eleven-year old boy was in intensive care after jumping from a third-floor window to escape the thick smoke during a dramatic escape caught on camera. The boy's parents and younger brother died in the fire, Skvortsova said.
The mall is located in the city of Kemerovo, a coal-mining center in Siberia.
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There was no immediate indication of the cause of the fire. Kemerovo residents said the mall was packed with children and their parents. "I shouted over the phone urging her to try to break out of the hall, but I couldn't do anything, the blaze was already confronting me", he said.
Four people were arrested and questioned by police Monday, including the head of the company responsible for servicing the fire alarm system and the technical director of the company that owned the shopping centre.
President Vladimir Putin late on Sunday offered his "deep condolences" to the families of the victims.
Kemerovo region has declared three days of mourning, and locals are leaving flowers and cuddly toys at a makeshift memorial near the complex.
Some were quick to blame lax regulations on Russia's fire safety inspection authorities, who have been accused of taking bribes to turn a blind eye to breaches.