It was found on Thursday morning in a pub car park in Newham, east London.
Mr Josovic, of Stamford Hill, carries out circumcisions for patients of all ages across the country.
The Evening Standard reported a friend of Mr Josovic saying a gang of three attackers had approached him as he left a house, stole his keys and watch, and made off in the car.
Hundreds of people shared an image of the vehicle on social media sites as part of appeals for its return.
No arrests are thought to have been made.
