Hennessey, who has been out for the last seven months, injured the knee in training on Monday and MRI scans confirmed he has caused further damage.
The Wales international played in three reserve matches and had been training fully for a month prior to the new problem.
"Of all of the players to have had such a surgery he has to have been one of the least likely to sustain a re-injury," Head of Medical Phil Hayward told the club's official website.
"His application over the last seven months has been exceptional and it is difficult to find an explanation as to why this occurred as he had met all of the benchmarks set and the surgeon was delighted with him.
"With such a surgery there is clearly a small percentage failure rate and it would appear he has unfortunately found himself amongst this unlucky few.
"The main focus now has to be on planning the next step for him which is something that will start immediately.
"With Wayne's exceptional work ethic and the support of the medical team here at Wolves there is no reason to think he will make anything other than a complete recovery from this setback.
"He will see the surgeon in the coming days when a decision will be made on the next steps for him towards recovery."
The player himself put on a brave face and paid tribute to the hard work of the medical staff at Molineux.
"It's hard because the lads in physio couldn't have done more for me, I've trained hard and there were no problems in the reserve games that I played in," said Hennessey.
"It was just one of those freak things that can happen and it's no use dwelling on it, nothing is going to change things. I'm just concentrating on getting fit again. I've done it once and I'll do it again."