Hennessey is set to be sidelined for three to four months although the bulk of that time will be taken up with the close season.
But the Wales number one will be unavailable for bottom-placed Wolves' final four games in their uphill battle to stave off relegation from the Barclays Premier League.
Wolves boss Terry Connor confirmed earlier in the day that Hennessey was undergoing an MRI scan after suffering the setback during Saturday's goalless draw at Sunderland.
Now sources close to the player are indicating Hennessey will miss the remainder of the campaign before recuperating in the summer.
It remains to be seen whether Hennessey has played his last game for Wolves should they be relegated after a three season spell in the top flight.
He is one of the players who is set to attract attention from other Premier League clubs after a fine season.
Hennessey has played 58 consecutive Premier League games since regaining his place from Marcus Hahnemann midway through the 2010-2011 season.
Dorus de Vries, signed last summer from Swansea as a replacement for Hahnemann, is poised to make his league debut in Sunday's home clash with title-chasing Manchester City.
Source: PA
Source: PA