Scans revealed Coutts dislocated his kneecap in the Capital One Cup defeat to Leicester City on Tuesday night and he will undergo surgery on Wednesday afternoon to repair the damage.
Derby manager Nigel Clough told the Derby Telegraph: "It is a big blow for him and for us, he was knocking on the door to get back in the side."
Coutts' injury comes as an added blow to Clough who already has Jeff Hendrick out until December following ankle surgery.
Meanwhile, James O'Connor faces months on the sidelines and looks set to undergo surgery on a thigh injury.
The defender, on loan at League One side Bristol City, sustained a 2cm tear in his thigh muscle during the 3-2 defeat at Swindon on Saturday.