The Wales international ruptured his anterior cruciate knee ligament during last weekend's goalless draw with Sunderland but did not realise the extent of the damage and finished the match.
Hennessey was due to have surgery on Wednesday and is expected to be out until October.
Wolves' head of medical services, Steve Kemp, told the club's official website: "Our worst fears have been realised."
Hennessey had made 58 consecutive Premier League appearances since being restored to the first team after regaining the number one spot from American Marcus Hahnemann in November 2010.
Dutch goalkeeper Dorus de Vries is now set to make his Premier League debut against Manchester City on Sunday.
Wolves manager Terry Connor said of Hennessey's injury: "Wayne just felt his knee during the game. He went to catch a ball right at the end and didn't think too much of it.
"But he felt slightly worse on Sunday so the medical guys wanted him to have a scan."
Wolves are five points adrift at the bottom of the table with four league games of the season left.
Source: AFP
Source: AFP