The Wales international suffered the injury during last weekend's goalless draw with Sunderland, although he did not realise the severity of the damage initially and completed the game.
Hennessey will have surgery on Wednesday and is expected to be out until October. Wolves' head of medical services, Steve Kemp, said: "Our worst fears have been realised.
Hennessey, whose chances of making the Great Britain Olympic team are also now over, had made 58 consecutive Premier League appearances since reclaiming the number one spot from Marcus Hahnemann in November 2010.
Dorus De Vries is set to make his Barclays Premier League debut against Manchester City on Sunday and is likely to keep the number one shirt for the remaining games of the season.
Wolves have also recalled Carl Ikeme from his loan spell with already-relegated Championship side Doncaster to provide cover for the Dutchman.