The 28-year-old was taken off on a stretcher during Wales' 27-13 victory over South Africa on 26 November.
It was initially said the British and Irish Lion, who has been capped 60 times by Wales, was set to miss at least the start of the Six Nations.
"It has been confirmed surgery is required. He will not play again until next season," said a statement.
Lydiate missed the summer tour of New Zealand after injuring a shoulder during Wales' defeat by England in May.
In his absence, one of Ross Moriarty or captain Sam Warburton, whom Lydiate filled in for against South Africa, is likely to start at six for Wales. James King could replace him for Ospreys.
Wales begin their Six Nations campaign against Italy in Rome on 5 February.
Ospreys and Wales flanker Dan Lydiate will miss the rest of the season with anterior cruciate ligament damage.