The 85-year-old Briton, speaking to WPP chief executive Martin Sorrell at an Advertising Week Europe conference, also hailed Russian President Vladimir Putin as a man who "should be running Europe" and expressed support for U.S. Republican presidential candidate Donald Trump.
The Russian Grand Prix in Sochi, a project close to Putin's heart, is the next race on the Formula One calendar and Ecclestone last year declared himself the president's "best supporter".
Formula One has not had a woman driver start a grand prix since 1976 and Ecclestone, who has caused offence in the past by comparing women to domestic appliances, triggered a backlash on social media.
"I don’t know whether a woman would physically be able to drive an F1 car quickly, and they wouldn’t be taken seriously," Ecclestone said in comments reported by the Guardian newspaper, the BBC and other media.
British driver Pippa Mann, who has competed four times in the Indianapolis 500 and is a race winner in the U.S Indy Lights series, fired back immediately.
"Sigh. #HereWeGoAgain," she said on Twitter.
"Perhaps someone should remind him that @IndyCar doesn't have power steering, and we're strong enough to drive those."
Asked by Sorrell, a non-executive director of Formula One and whose grandparents came from Russia, whether immigrants had contributed to Britain, Ecclestone replied: "They have not."
Britain's triple Formula One world champion Lewis Hamilton is the grandson of immigrants to Britain from the Caribbean island of Grenada.
The NBC Sports website reported the comments under the headline "Ecclestone says more Ecclestone type controversial things".
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