The Welsh international had been back in training over recent weeks, with a return to senior action believed to have been pencilled in for December.
However, the club have now confirmed that 25-year-old aggravated the ligament on Monday and may now require an operation to correct the problem.
Despite the disappointment, Hennessey has vowed to bounce back as soon as possible.
"It's hard because the lads in physio couldn't have done more for me," he told the club's official website. "I've trained hard and there were no problems in the reserve games that I played in.
"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. So I'm just concentrating on getting fit again. I've done it once and I'll do it again."
Hennessey joined Wolves as a trainee from Manchester City in 2003.