A district judge said the incident in Mr Balls's Morley and Outwood constituency, in West Yorkshire, was "at the lower end of the scale of seriousness" and rejected the option of a total driving ban.
The former Education Secretary touched the bumper of another car as he was moving out of a car park next to the Labour Unity Club in Morley in April, causing minor damage.
He already had three points on his licence after he went through a red light in central London in 2012.
Mr Balls did not attend the hearing at Leeds Magistrates' Court yesterday.
District Judge Roy Anderson read a letter from Mr Balls's solicitors admitting the offences of failing to stop and failing to report an accident.
He said Mr Balls's account was that he did not realise at the time that he had caused any damage to the parked Peugeot 308 as he moved out of the car park in his Ford Mondeo.
The district judge ordered the Shadow Chancellor to pay a £900 fine plus a £90 Government surcharge and £85 prosecution costs.