Williams, who is currently on loan at Ipswich Town from Crystal Palace, sustained the problem against Watford on Saturday, and will miss the Euro 2016 Group B qualifier in Brussels on Sunday.
A heavy challenge from Joel Ekstrand caused the injury to the 21-year-old, with a scan on Monday confirming he is set for a few weeks on the sidelines.
Williams' only appearance of the qualifying campaign so far came in the goalless draw with Bosnia-Herzegovina in October, and he is frustrated at not being able to add to that at the weekend.
"It's always disappointing to miss out on games," he told Ipswich's official website. "It's exciting times for Wales.
"It's probably our best chance to qualify in a while.
"We've had two wins and a draw against a good Bosnia side. All the home nations have started well and we will be looking to qualify."
Wales sit top of Group B after an unbeaten start to their campaign, however Belgium provide their sternest test so far.
