A total of 17 people, some pedestrians and some passengers on the bus, were found injured.
Two people were treated at the scene while 15 were taken to and remain in hospital.
This includes the driver of the bus.
There were no life-threatening injuries reported.
No arrests have been made and an investigation has been launched.
Pictures from the scene show a number of emergency vehicles including police cars, ambulances and a fire engine in attendance.
The front of the bus is visibly damaged, with the windscreen smashed.
The road remains closed with all vehicles being diverted from the area, the Met said.
Emit Suker, 47, told the PA news agency: “It (the bus) was coming from Westminster – it was going really fast and came off the road.
“There were about 15, 16 people inside the bus. People were screaming – it was terrible.”
Another eyewitness told PA: “I heard a massive crash, came outside and there was a woman on the floor with loads of people around her.
“Lots of people from the gym had run out to help her.”
A trail of diesel running down Allington Street has forced police to ban smoking in the area over fears of an incident.
A London Ambulance Service spokesperson said: “We were called at 8.20am today to reports of a road traffic collision on Victoria Street, Westminster.
“We have sent resources to the scene, including ambulance crews, advanced paramedics, a paramedic in a fast response car, a clinical team manager, an incident response officer and a command support vehicle. We’ve also dispatched London’s Air Ambulance.
“The incident is ongoing and we are working with our emergency services partners.”
Rosie Trew, TfL’s head of bus service delivery, said: “Our thoughts are with the people who have been injured following a bus incident at Victoria Street.
“We are working with the police and the operator, Transport UK, to urgently investigate this incident.
“This must have been a distressing incident for everyone involved and we have support available for anyone affected.”
Two pedestrians have been killed in bus crashes in Victoria in recent years.
Catherine Finnegan, 56, from County Galway, Ireland, died after she was hit by a double-decker bus at Victoria bus station in January last year.
In August 2021, Melissa Burr, 32, from Rainham, Kent, was killed at the station after bus driver Olusofa Popoola accidentally accelerated into the back of a stationary bus, shunting it into her.
Ms Burr was using a pedestrian walkway at the bus station and crossed towards the door of a 507 bus parked at its stop before she was hit.
Popoola, of Peckham, admitted causing Ms Burr’s death by careless driving and said he had pressed the accelerator instead of the brake by mistake.
He was sentenced at the Old Bailey to 18 months imprisonment, suspended for two years.
Victoria bus station was closed in late 2023 for works designed to improve pedestrian safety and accessibility for partially sighted passengers.
Problems highlighted included an unconventional layout of pedestrian crossings, use of markings and a lack of tactile paving, as well as one crossing that directed pedestrians into a bus stop.
