Biggar, one of the standout performers at last year's Rugby World Cup, sustained the injury early in the 16-16 draw in Dublin and, despite playing on with heavy strapping for several minutes, was forced off midway through the first half.
"Indications are that the injury is not considered long term and decisions over his availability for this weekend will be made later in the week," the WRU said on Tuesday.
Biggar was replaced by Rhys Priestland who kicked 11 points as Wales hit back from 13-0 down to force a draw in their tournament opener.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Priestland, capped 41 times but now second choice behind Biggar, announced in October that he was taking a sabbatical from internationals to focus on club rugby with Bath.
But he reversed his decision in December and made himself available for selection.
(Reporting by Justin Palmer, editing by Ed Osmond)
