Television pictures showed the bus had been cut into two pieces and turned into a tangle of black wreckage by the force of the crash, one of the deadliest accidents around the Russian capital in recent years.
Police said it was thought to have occurred when the truck turned onto a main road and ploughed into the bus.
The head of the capital's health department, Georgy Golukhov, told the RIA Novosti news agency that injuries had been especially severe as the bus passengers were also hit with the gravel the truck was carrying.
Moscow deputy mayor Pyotr Birukov said that the driver, a 46-year-old Armenian, had been fined for traffic violations six times over the last year.
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The driver, who survived the crash, has been hospitalised and is being interrogated by police, Birukov added.
Of the injured, around 25 are still hospitalised with 15 in a serious condition and the other 10 with injuries of medium seriousness, the RIA Novosti news agency said, quoting the health ministry.
Earlier death tolls rose rapidly after several injured victims died in hospital.
The bus was travelling on a regular public transport route from Podolsk to Zhokhovo in the Moscow region and was packed with some 60 passengers.
A huge traffic jam ensued as emergency services blocked off the road with police handing out water to stranded drivers on a hot summer's day.
Russia has one of the world's worst road safety records with some 25,000 people losing their lives in traffic accidents every year, although the government is seeking to improve the situation with tough measures including a zero tolerance ban on drink driving.