The 32-year-old, who has scored 10 league goals, was offered reduced terms in January but turned the deal down.
Meanwhile, Paul Ifill, John Oster and James Scowcroft are among nine first-team players that are being released.
The other players leaving Selhurst Park are Scott Flinders, Carl Fletcher, Ryan Carolan, James Dayton, Jamie Smith and David Wilkinson.
Kuqi has turned his fortunes around at Selhurst Park after being placed on the transfer list last year by Warnock for making an offensive gesture at Palace fans, who cheered his substitution following a poor performance in the 2-0 defeat against Wolves.
Despite seemingly starting the 2008/09 season with little chance of figuring in Warnock's plans, the former Ipswich and Blackburn forward impressed for Palace after winning back his first-team place during an injury crisis.
Midfielder Fletcher is currently on loan at Plymouth, where he has made 13 appearances and scored one goal.