Holmes suffered a serious gash to his knee when he collided with an advertising board during North End's draw with Bournemouth on Saturday, with the wound requiring 45 stitches.
"Lee is going to be out six weeks, I would suspect," Westley (pictured) told the club's official website.
"He had an operation on Saturday night and it all went well, but he is that distance away from first team action.
"He is going to be in a splint for two weeks, with 45 stitches in the injury. It is a case of the wound healing and then rehabilitating the leg.
"He's going to lose a lot of fitness during that time, so he has six weeks to full training and then we have to get him fit."