The 20-year-old suffered ligament damage in PSV Eindhoven's defeat to Feyenoord on Saturday.
Willems, who has been linked with Manchester United and Arsenal, seemed to be a certainty for Louis van Gaal's 23-man squad after starting throughout their qualification campaign when fit.
In a statement on the PSV website, the club said: "Jetro Willems is to miss the rest of PSV's season after having been ruled out for several months with knee ligament injury.
"PSV's medical staff reports that the 20-year-old left-back has damaged his knee. Willems hopes to be fit again for pre-season training."
Willems was the youngest player at the 2012 European Championships.