The Late Late Show host was the MC at an AmfAR charity gala in front of stars including Julia Roberts and Tom Hanks in Los Angeles when he said: "It's a beautiful night here in LA. So beautiful, Harvey Weinstein has already asked tonight up to his hotel to give him a massage."
In footage of the monologue posted on Twitter, it can be heard that the gag received a mixed reaction.
Corden responded by telling the audience: "I don't know whether that groan was because you like that joke or you don't like that joke.
"If you don't like that joke, you should probably leave now."
He continued: "It has been weird this week though, watching Harvey Weinstein in hot water.
"Ask any of the women who watched him take a bath, it's weird watching Harvey Weinstein in hot water.
"Harvey Weinstein wanted to come tonight, but he'll settle for whatever potted plant is closest."
When the last remark was met with loud groans, he can be heard exclaiming: "Oh, come on!"
The jokes were widely condemned on social media where one user said: "If the problem is Hollywood not taking systemic sexual abuse seriously, the solution does not involve James Corden making light of the issue."
Another said: "I've always made it my mission to tell every American I meet that we hate James Corden in the UK. Now they know why."0
Another said: "If today is the day James Corden is exposed for being the talentless and unfunny sycophant that he is, then hurray."
James Corden offered an apology on Twitter following the backlash, claiming "sexual assault was no laughing matter".
"To be clear, sexual assault is no laughing matter. I was not trying to make light of Harvey’s inexcusable behavior, but to shame him, the abuser, not his victims," Corden wrote on Twitter.
"I am truly sorry for anyone offended, that was never my intention."
Corden's first big break in Hollywood came when he played Britain's Got Talent winner Paul Potts in The Weinstein Company's film One Chance.
Last month, the chat show host said he was "disappointed in himself" for cosying up to former White House press secretary Sean Spicer at the Emmy Awards, after a photograph emerged of him kissing Spicer on the cheek.
