The 20-year-old, the youngest player to appear at a European Championship tournament two years ago, suffered a cartilage tear, PSV said in a statement on their website (www.psv.nl).
A scan on the knee revealed damage that will keep him out for "several months," the statement added.
"His season is prematurely ended and his focus will now be on getting ready for the next season."
Willems won the last of his 11 international caps in a friendly against Japan in November.
The Dutch play holders Spain, Australia and Chile in Group B at the World Cup finals in Brazil starting in June.
(Reporting by Mark Gleeson; Editing by Tony Goodson)