It is thought he is the eighth Russian general to have died during the war.
Frolov was given a military funeral at the Serafimovskoe Cemetery in St Petersburg on Saturday.
The St Petersburg governor paid tribute to the Russian commander who died on the battlefield.
“Today we say goodbye to a real hero,” Beglov said.
“Vladimir Petrovich Frolov died a heroic death in battle with Ukrainian nationalists. He sacrificed his life so that children, women and old people in Donbas would no longer hear bomb explosions. So that they stop waiting for death and, leaving home, say goodbye as if it were the last time.”
It was not revealed when the general died or where, though he was leading the eighth army which had been fighting in Mariupol for weeks, according to reports.
His death is the latest blow to Putin since he declared war on Ukraine in February.
It comes as Ukrainian soldiers appeared to defy a Russian ultimatum to lay down their arms on Sunday in the port of Mariupol which Moscow said its forces had almost completely seized.
Ukrainian fighters showed no sign of surrender.
The Russian military has refocused its ground offensive on the eastern Donbas region.
Around four million Ukrainians have fled the country while cities have been bombed and thousands killed.