Both the sporting director and manager Malky Mackay, who worked together at Cardiff City and had been close to a reunion at Selhurst Park, are set to be investigated by the FA.
Reports emerged Wednesday that Moody and the former Cardiff City manager, who worked together at the Welsh club, had allegedly shared racist, sexist and homophobic texts, which the FA will now look into.
And Moody, who had been involved in Palace's search for a new manager following Tony Pulis' sudden departure just before the start of the season, has now decided to step down from his position at the club amid the controversy.
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"In light of the events of yesterday, sporting director Iain Moody has tendered his resignation and it has been accepted with immediate effect," read a statement on the club's official website. "There will be no further comment from the club on this matter."
Mackay had been a frontrunner to succeed Pulis at Selhurt Park but the allegations, coupled with Moody's resignation, mean that Palace will now look elsewhere in its search for a new manager.
Moody joined the Eagles in November 2013 after being axed by controversial Cardiff owner Vincent Tan, who infamously replaced the head of recruitment with 23-year-old Kazakh Alisher Apsalyamov.
The two clubs have endured strained relationships since, with Cardiff accusing Moody of obtaining its starting XI prior to a Premier League encounter that the Eagles won 3-0, with the Premier League eventually fining Palace 30,000 euros.