The CNN host likened Schwarzenegger's fathering of a secret love child to golfer Tiger Woods's string of extramarital affairs because both celebrities reportedly attempted to cover up their misdeeds.
Morgan told Access Hollywood Live: "It's like Tiger Woods - death by a thousand cuts. You leave these things, and more and more stuff comes out… He's made a catastrophic error here and it's had big repercussions."
He added that Schwarzenegger should further acknowledge the error of his ways in order to improve his public image.
"I happen to still like the guy, and he's been very good to me and if he wanted to do a mea culpa on my show, I would recommend him to do that," he said. "There's a power of being honest and open about these things."
Morgan recently admitted to tensions with his fellow America's Got Talent judge Howie Mandel, describing the comic as "the most annoying man" alive.
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Watch Piers Morgan discuss Arnold Schwarzenegger's admission of infidelity below: