The midfielder's contract expired at the end of June, and he was keen to extend his one-year stay at Selhurst Park.
A statement on the Palace website read: "Moritz signed a one-year deal at Selhurst Park, which expired at the start of July - and the club have decided not to offer an extended deal to the player.
"Moritz made a total of 32 appearances for Palace last season, including coming on as a substitute against Watford in the Championship Play-Off Final at Wembley. He found the net on five occasions.
"Crystal Palace Football Club would like to place on record its sincere thanks to Andre for his service and commitment during the 2012/13 season. We wish him all the best for the future."