The vessel carrying armed officers hit the structure at around 3.40pm on Friday, according to the Metropolitan Police.
The Met said a number of officers “entered the water, but were recovered”, following the crash that involved a boat from its marine policing unit.
The Met also said more officers responded alongside the London Ambulance Service and London Fire Brigade.
The force continued: “We understand five officers were injured and are receiving treatment. We await an update on the extent of their injuries.
“At this stage, we don’t believe any members of the public were involved or injured.”
The Met said the circumstances of the incident will be “thoroughly reviewed, but at this stage our priority is the wellbeing of the officers involved”.
Following the crash, crowds of onlookers watched the aftermath from the bridge before being moved from the area.
Surrounding roads and two entrances of nearby Westminster Underground station were also closed.
Mother and son Cecilia Lusevic, 56, and Mateo Bilis-Lusevic, 12, said they heard a loud bang when the police boat crashed into Westminster Bridge.
The visitors from Chile were on a Thames tour boat on the north side of the central London bridge when they saw the incident. They were evacuated from their vessel shortly after.
Mateo said: “Two boats were riding extremely fast through the water. Suddenly, I heard a boom. I was looking towards the boat, and I heard a boom.
“Then three people went flying into the water and one of the people was really hurt.”
He said the officers were in the water for around 10 minutes and a life ring was thrown for one of them.
A Port of London Authority spokesperson said: “We are aware of an incident involving a police vessel at Westminster Bridge.
“We are supporting the response and providing assistance where needed, working closely with the Metropolitan Police, HM Coastguard and partner agencies to manage the situation.”
