The Cambridge academic said Mr Corbyn was a “disaster” for the party despite having "sound" policies and having his heart "in the right place".
The Labour-backing physicist said he would vote for Mr Corbyn but that he should quit “for the sake of the party”.
“His heart is in the right place and many of his policies are sound but he has allowed himself to be portrayed as a left-wing extremist.
“I think he should step down for the sake of the party.”
Professor Hawking's comments come shortly after shadow chancellor John McDonnell wrote an article claiming that a “soft coup” was under way by opponents of Mr Corbyn inside and outside the party.
Labour has struggled in the polls of late, with the Conservatives reaching an average lead of 16 points.
Mr Corbyn's personal ratings have also bombed, despite his re-election as Labour leader for a second time in autumn last year.
Last week the party lost a by-election in the Copeland constituency, ceding the seat to the Conservatives for the first time in 80 years. It won a concurrent by-election in Stoke with a reduced majority.
Additional reporting by PA