The car, a white Mercedes, crashed into a wall located on Daniel Hill, Upperthorpe at about 1am.
Following the collision, the car drove off and was found abandoned a couple of streets away by officers who are now forensically examining it for evidence.
A South Yorkshire Police spokesman said the Mercedes hit a parked silver Ford KA which went through the wall, located on a verge, and fell 10ft on to an external gas meter outside a nearby house.
This is believed to have caused a gas leak.
British Gas and South Yorkshire Fire and Rescue are reportedly still on the scene.
A spokesman for South Yorkshire Fire and Rescue said: "The car was clearly travelling at speed. It had not navigated the corner well, and crashed."
"The car was still on the road after the collision, but limped away because of the damage caused and was found a couple of streets away."
No-one is believed to have been injured in the collision.
Anyone with information is asked to call South Yorkshire Police on 101, quoting incident number 67 of March 11, 2018.