Lynton Yates said they should catch a bus instead, while cyclists should "go back to the pavements".
Mr Yates published the leaflet as part of a canvassing campaign for the general election, but UKIP has now suspended his candidature.
The BBC has tried to contact Mr Yates but he has not responded.
Mr Yates, who remains a Leicestershire county councillor for UKIP, also stated in the leaflet that he would send prisoners to overseas jails to reduce costs.
A statement from UKIP said: "Lynton Yates' views do not represent UKIP policy.
"He has apologised for any offence caused and was today suspended as a [general election] candidate."
UKIP earlier confirmed the leaflet was published by Mr Yates, following suggestions it was a hoax or spoof.
Shadow health minister Jamie Reed, a Labour MP, said: "It's beyond a joke now. Not so much a political party but a stag night out of control."
Mr Yates was a candidate for the Charnwood constituency in Leicestershire.
A photo of his leaflet was posted on Facebook by a blogger called Mum Juice, then spread more widely on Facebook and Twitter by a satirical group called Atos Miracles.
The leaflet said: "We could likely remove six million cars from the road if benefits claimants were not driving.
"Why do they have the privilege to spend the tax payers hard earned money on a car, when those in work are struggling to keep their own car on the road?
"These people really could catch a bus!"
On the topic of the cost of keeping criminals in prison, it continued: "I personally would look to overseas countries who could tender for their incarceration.
"I'm sure they could dramatically reduce this cost to the taxpayer."
A UKIP member has produced a leaflet calling for all "benefits claimants" to be banned from driving to free up space on the roads.