Russian state investigators said four people had been detained over the fire, including the owners and lessees of outlets inside the shopping mall. The report also says that an additional 43 people have been injured in the blaze.
The first reports of the fire at the Winter Cherry mall started coming in on Sunday afternoon, reports Sputnik news.
Tass said the fire started on the top floor but the cause was not immediately known.
Numerous victims in the coal-mining city of Kemerovo were children.
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The fire broke out at about 17:00 local time on Sunday (11pm NZ time).
It took fire fighters nearly 16 hours to extinguish the blaze. All the animals are reported to have died.
Winter Cherry was one of Kemerovo's most popular entertainment centers for families with children, with its own indoor skating rink, petting zoo and trampolines and a movie theater with several screens.
Health Minister Veronika Skortsova said from the scene that 11 people were in hospital, including an 11-year-old boy in a serious condition. The investigators have launched a probe into possible negligence and violations of the fire safety rules.
However, Rossiya 24 TV, a national broadcaster, said an electrical fault was the most likely cause - as in most previous deadly fires in Russian Federation.
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Negligence, cost-cutting, corruption, and the thwarting of safety rules are blamed for causing or aggravating the human toll from blazes in Russian Federation, where the death rate from fires is far higher than in most Western countries.
Kremlin spokesman Dmitry Peskov told reporters on Monday it was too early to draw conclusions about whether local officials failed in Kemerovo.
Alexander Lillevyali, who lost 11-year-old twin daughters and a five-year-old daughter in the fire, told Meduza news site that his children called him to say they could not open the cinema's door.
"My daughter kept calling me". As a result, many companies prefer to pay bribes instead of complying with outdated and excessive regulations, including fire safety rules.
The Russian president "expressed his deep condolences to the relatives and loved ones of those who died", the Kremlin said in a statement.
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