"Rescuers took nine people out of the sunken bus...," the emergency situations ministry said on social media.
"Unfortunately, three people died," and two others were in a serious condition, the ministry added.
The ministry said divers were attaching slings to lift the bus out of the water.
The police earlier said that there were "around 20 people" on board the bus, which crashed into the Moyka River in the historic city centre.
Closed-circuit video images apparently showing the crash were broadcast on Russian media.
The video showed the bus veering sharply in the road before crashing from a bridge and sinking within seconds.
