The blaze started at around 11am local time on an upper floor of the Winter Cherry complex in one of the country's key coal mining cities.
Many of the victims were in a multiplex cinema - where the roof collapsed.
Video posted on social media showed people jumping from windows to escape the flames.
A spokesman for the coordination of emergency services explained that a massive operation took place with over 600 personnel deployed in the rescue effort.
Firefighters tackled the blaze covering more than 1,000 square metres of the centre for more than 17 hours.
The cause of the fire is not yet known and authorities have launched an investigation.
Kemerovo, a key coal-producing area, lies about 3,600km east of Moscow.
Austrian Chancellor Sebastian Kurz offered his sympathies with a message on social media.
"My condolences to the families and friends of the victims of the terrible fire in the shopping mall in Kemerovo. It is tragic that so many children are dead or missing. I wish a speedy recovery to those injured" he wrote.
It was the deadliest blaze in Russia in recent years.