The bus was travelling through the town of Juvisy-sur-Orge southeast of the French capital when it veered off the road and fell into the Seine "under circumstances that remain unclear at this stage", prosecutors told AFP.
"The driver and three other people were on the bus," prosecutors added.
"They have all been rescued," they said, adding that the police have opened an investigation.
Officials did not provide details on the condition of the rescued people.
The bus was completely submerged under water near a bridge while the parked car struck by the vehicle also ended up in the river, an AFP journalist reported.
Several rescue boats, a drone and helicopters were deployed as part of a recovery effort.
"The casualty figures are currently being finalised," the prefecture said in a statement. "Significant emergency resources have been mobilised."
Local lawmaker Claire Lejeune said that the bus was being driven by a trainee under instruction.
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