There was also a further setback for lock Dan Tuohy, who will miss Saturday's final Pool 4 trip to Castres where Ulster require a first competitive victory on French soil if they want a home draw in the quarter-finals.
New Zealand-born Williams (below) will miss at least five games, with Ulster hoping he will be ready to face Edinburgh in a Pro12 game on March 22, or Leinster the following week, in preparation for the Heineken Cup quarter-final in April. Plucked from relative obscurity by Anscombe, the No 8 has scored seven tries for Ulster this season.
Better news is that Craig Gilroy and Paddy Jackson are both expected to be fit, although Ireland winger Gilroy is expected to go through a concussion protocol test before he gets the all-clear following a bang to the head. Jackson turned an ankle, but he is responding well to treatment.
Jared Payne suffered discomfort after the game against Glasgow following a groin problem, but he is also expected to be ready for the trip to France.
Prop forward Adam Macklin is likely to be out a few more weeks after he sustained a knee injury during the Ravens 12-8 defeat to Bristol in the British & Irish Cup.
Skipper Chris Henry says the job in Europe is still only half done.
"It's great that we have qualified but I think the most important thing now is that we have a home quarter. That's everything," said the Ireland flanker.
"Our goal at the start of the year was to be competing with the best, to be up there with Leinster and Munster. We have talked about that for two or three years.
"As players it is at the front of our minds, we want to win something, we are ambitious. We want players playing for different representative teams.
"I felt straight up after the Heineken Cup last year that this team was going to be better this year.
"Coming through losing the final just makes you want to get back there and win it a little bit more."