Moody and former Cardiff manager Malky Mackay are alleged to have exchanged derogatory texts during their time at the Welsh club after reports emerged on Wednesday.
A former head of recruitment at Cardiff, Moody left his position late last year and joined Palace, with Mackay departing the club soon after.
Mackay's chances of taking the vacant Palace job are believed to have ended amid suggestions of further legal action and, due to the ongoing off-field controversies, Moody has opted to leave his post.
A statement from Palace on Thursday read: "In light of the events of yesterday, sporting director, Iain Moody has tendered his resignation and it has been accepted with immediate effect."
Moody is said to have been at the centre of a spying row between Cardiff and Palace prior to their Premier League fixture in April, which the London club won 3-0 in south Wales.
Palace were fined for the incident earlier this week, with Moody alleged to have contacted former colleagues at Cardiff for confidential information - an allegation he denies.
Cardiff owner Vincent Tan oversaw the exits of both Moody and Mackay last year and the stream of disagreements and legal rows have continued apace since then, with the Football Association to investigate a dossier from Cardiff into Mackay and Moody's alleged misconduct.
Mackay dropped his claim for wrongful dismissal and apologised to Tan in May after the Malaysian businessman came under much criticism for replacing the Scot with Ole Gunnar Solskjaer.
Cardiff were duly relegated to the Championship with Solskjaer at the helm.
