Rescue workers initially reported one death on Thursday, according to TASS state news agency.
Twenty-one seriously injured victims ended up in hospital while 84 adults and 10 children were sent home after receiving initial treatment.
An eyewitness posted a video of the dramatic incident online.
It shows a tram rolling at high speed down the street towards the Tom River without braking.
The doors spring open and passengers are thrown onto the street into the moving traffic.
The vehicle only came to a stop after reaching an uphill bridge ramp, where it collided with another tram.
Possible causes of the accident include brake failure or driver error.
However, Mayor Dmitry Anissimov also said that the trams in his city were up to 40 years old and 80 per cent to 90 per cent worn out.
He also said the city's track infrastructure needed to be renewed.
Kemerovo, a mining city, is located about 3000km east of Moscow.
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