His condition was not thought to be “life-threatening”.
The gunshot happened as armed London police stopped a car in connection with a fatal stabbing shortly after midday in Southampton.
Three men were arrested at the scene.
Now the Independent Office for Police Conduct (IOPC), the police’s watchdog, has opened an investigation.
Graham Beesley, regional director, said: “The discharge of firearms by police officers is relatively rare but where potentially lethal force has been used, it is important that we carry out an independent investigation into the circumstances.”
A Scotland Yard spokesperson said: “On Sunday, 24 July, firearms officers were following a vehicle – that had entered London – which was believed to be involved with an ongoing investigation being led by another police force.
“At about 8.30pm, the vehicle was stopped on Beaufort Road at the junction with Kings Road.
“A police firearm was discharged.
“One of the occupants of the car sustained a gunshot injury to his hand. He has been taken to hospital for treatment; his injury is not life-threatening.”
The Met said the Directorate of Professional Standards had been informed and confirmed that the IOPC had launched its investigation.
Beaufort Street was reopened after the incident, having been closed between Battersea Bridge and King's Road, with bus diversions previously in place.
Hampshire Police are leading a criminal investigation into the fatal stabbing in Southampton.