The comedian, 46, admitted the offence, which happened near his Kent home, at Maidstone magistrates on Thursday.
He had previously pleaded guilty to a related charge of drink-driving after crashing into a stationary car while three times over the legal limit.
The smash happened in the village of Boughton Malherbe on 25 March.
Since admitting the drink-drive charge on 7 April, Reeves, whose real name is Jim Moir, has been subject to an interim driving ban.
In March, his vintage Jaguar hit a Peugeot 106, in which one of his neighbours was sitting.
The Jaguar then careered up a verge into a fence. Reeves drove away.
The court heard he had been out to get cigarettes from a pub and did not notice that he had hit the parked car.
Tests later showed he had 117 micrograms of alcohol in 100 millilitres of breath. The legal limit is 35 micrograms.
The court heard he had been drinking gin and tonics during the day while writing a radio script, and then had a glass of white wine after driving to the pub.
Rehabilitation course
His legal adviser said Reeves did not have a drink problem, and only drank socially, adding this was an isolated case.
Sentencing the comedian, chairwoman of the bench Lizzie Hughes said he could have faced a jail term, but would receive a lower punishment because of his early guilty pleas, contrition, and lack of previous offences.
The driving ban will be reduced to two years if he pays 」200 to complete a drink-driving rehabilitation course.
Reeves told the court he planned to take part in the course.
'Not work-shy'
As he left the proceedings with his wife, Nancy Sorrell, he said he was relieved the case was over.
Asked whether he was looking forward to the community service, he said: "In a way, I am, yes.
"I am not work-shy and I'm not afraid of a bit of hard work."
He said: "I'm completely remorseful, and penitent and it was a stupid, stupid thing to do."
