The number 59 double-decker bus swerved to avoid another vehicle and hit the tree in Kennington, South London.
The tree was embedded in the front of the bus and emergency crews had to use cutting equipment to gain access to one side of the vehicle to release two people who were trapped.
London Fire Brigade station manager Clive Robinson, at the scene, said: “We are working to release two people who are trapped on the top deck of the bus.
“A number of people have been injured and are being taken care of by paramedics.”
Metropolitan Police traffic sergeant Richard Sutton said two people were critical, including the girl. Two others were seriously hurt, he said. And two off-duty police officers were injured, one with a “heavily suspected” broken arm.