Shaw was shown on TV eating a pie, which he has since claimed was a cornish pasty, after a bet had been promoted by the club's one off sponsors the Sun via their Sun Bets brand.
The club's back up goalkeeper has come in for criticism and is being investigated by the government's Gambling Commission and the Football Association following the incident.
"Wayne has offered his resignation to the chairman this afternoon and that has been accepted. It's a very sad end to what was a very good story," Sutton manager Paul Doswell told Sky News.
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Wayne Shaw has resigned from Sutton after the pie incident
Sutton United fan invades the pitch during FA Cup clash with Arsenal
Mon, February 20, 2017
A Sutton United fan invaded the pitch during their FA Cup clash with Arsenal on Monday
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A streaker invades the pitch during Sutton's FA Cup clash with Arsenal