The dogs were found in the vehicle in the Met's dog training centre in Keston An officer was later found by colleagues in the Newham area, east London, suffering a hand injury.
Commissioner Sir Paul Stephenson said he was "very saddened" by the deaths.
The Directorate of Professional Standards has begun an inquiry.
Disciplinary inquiry Sir Paul added: "I'm very saddened by what's happened and we are taking it very seriously.
"There's an investigation going on. It's being led by the RSPCA, with a separate internal disciplinary investigation going on in the force."
Officers forced their way into the car after being alerted.
The working Belgian Malinois and a German Shepherd puppy were taken from the dog training centre to an emergency vets, where both later died.
Police have not named the officer linked to the incident, but confirmed a policeman was found with injuries following the discovery of the dead canines.
It is not known if they were self-inflicted.
The Met Police spokesman added: "The officer was located in Newham borough suffering a hand injury.
"He was taken to an east London hospital as a precaution and is currently receiving medical treatment."
The RSPCA, which is also investigating the incident near Bromley, where temperatures reached almost 30C on Sunday, advised people not to leave dogs in vehicles "for any length of time" during hot weather.
The Independent Police Complaints Commission has been made aware of the incident and the subsequent investigation.
The Met has about 250 working dogs and the animals at the training centre in Keston were either donated or bred on site.
The centre was set up in 1954.
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