Curtis, although not cup-tied, has not joined United in time to play in their FA Cup quarter-final against Leeds United on Sunday because of the seven-day deadline for loan signings.
United boss Neil Warnock told the club's official website: "The opportunity came along to sign John and I had to make a quick decision at the weekend because Crystal Palace were interested.
"I haven't guaranteed him a first-team place but he's got a great attitude and can play both full-back or centre-half which is a great help."