Reid was appointed first-team coach alongside Roy Hodgson last season and helped guide the club to an 11th-placed finish.
Reid announced the news on Twitter, saying: "Just want to say a massive thanks to everybody at [Crystal Palace Football Club] for an unbelievable time at the club.
"A special club with special fans. Unfortunately for personal reasons it's time to take a break for a while. Been a privilege to work alongside the staff and a fantastic group of players."