The Ukip leader said the possibility of attacks like those seen in Cologne in Germany will be “the nuclear bomb” of the referendum campaign.
But Treasury Minister and Leave campaigner Andrea Leadsom said his comments were wrong.
The Tory MP told Pienaar’s Politics BBC Radio 5 Live: “I don’t like that sort of campaigning at all.
“However we know for a fact that there was an appalling experience for women over in Germany over the Christmas period.
“I do not approve of that sort of campaigning, I do not believe in outright blatant scaremongering so I think it’s really, really regrettable.
“I haven’t seen it and I wouldn’t support suggesting if you vote to remain you’d be raped. Obviously that is just an outrageous thing to say.”
Brexit campaigner Michael Gove also refused to associate himself with Mr Farage’s comments.
The Justice Secretary told ITV’s Peston on Sunday: “He’s made those remarks and I haven’t made remarks like that and I won’t make remarks like that.”
Mr Farage made headlines during the general election campaign last year when, during a TV debate, he claimed the cost of drugs for foreign HIV patients should instead be spent on cancer drugs for deserving Britons.
“The nuclear bomb this time would be about Cologne,” he told the Sunday Telegraph.
In January, reports emerged of allegations that hundreds of women were groped, robbed and intimated at the German city’s central station on New Year’s Eve.
“There are some very big cultural issues,” Mr Farage said.
Asked whether mass sex attacks like those in Cologne could occur in the UK, he said: “It depends if they get EU passports. It depends if we vote for Brexit or not. It is an issue.”