Firefighters tackled the blaze at the parked Mercedes A180 SE on Monday after it was set alight between 11pm and 11.30pm.
Portsmouth police are now investigating the arson attack.
A Hampshire police spokeswoman said: ‘Officers investigating are keen to speak with anyone who may have been in the area at the time or who has any information.
‘Were you in the area at the time? Perhaps you have dash-cam footage of the area or the car?’
Call 101 with any information quoting 44210057954.
Alternatively, call Crimestoppers anonymously on 0800 555 111.