The club have confirmed that O'Hara has undergone surgery on the groin injury which has sidelined him since the home defeat to Blackburn over three weeks ago while Craddock has also gone under the knife in a bid to cure a long-standing hamstring problem.
Former Tottenham man O'Hara is expected to miss between six and eight weeks while the club predict Craddock will be out for at least five.
"Both Jamie and Jody have undergone successful operations," said head of Wolves' medical department Steve Kemp.
"Jamie has been struggling with a groin problem for several months and every attempt had been made to maintain his availability whilst trying to strengthen and rehabilitate the groin at the same time. Unfortunately this was not possible and it is hoped that surgery should rectify the problem although it means he will be out for a further six to eight weeks.
"Jody has also undergone a minor procedure on a persistent hamstring problem and, while it is always difficult to predict, he is hoping to be available again within five weeks if his rehabilitation progresses well."