But a Downing Street spokeswoman stressed the wandering feline, who went missing earlier this year, was not seriously hurt in the accident on Thursday night.
The news came as cat enthusiasts around the globe celebrated World Cat Day.
It is understood Freya was "clipped" at the Ministry of Defence end of the street, but it is not yet clear whose car was involved. She had to be taken to the vet, but is recovering and expected to be on her way home soon.
The Chancellor was said to be "grateful" for all those who helped in the wake of the incident and will pay any bills out of his own pocket.
In May, the cat was chauffeur-driven home after turning up frightened and lost in Vauxhall where she was found by homelessness outreach worker Kate Jones who identified her from the tag on her collar.
Ms Jones, who works with Thames Reach's London Street Rescue, said she had lots of experience helping the homeless in London - but that it was the first time she had helped a cat find shelter.
Freya spent the night at Ms Jones's home before being collected by Downing Street officials. She had somehow travelled south of the River Thames and at least two kilometres (1.5 miles) before being found.
Ms Jones later posted a picture of the cat with a note to remind Mr Osborne that while she had been given shelter for the night in this instance, most homeless people are not so fortunate.