Coach Warren Gatland confirmed Biggar was ruled out after he took a blow for the second successive game as Wales beat Fiji 29-17.
“Josh just got a dead leg and Jonathan with his knee, something similar. But you never know with knees,” he said.
All three players were likely to have been rested for Sunday’s match against Uruguay with Wales already assured of a quarter-final place.
Biggar was hurt when he clashed with Wales full-back Liam Williams during the second half against Fiji.
The Northampton Saints stand-off failed a head injury assessment (HIA) in Wales’ previous match against Australia.
Gatland said Biggar would be assessed before the quarter-final.
“He didn’t do a HIA against Fiji, he was just removed from the field,” said Gatland.
“It means that he won’t be in consideration for Sunday and he will have to go through protocols.
“We’ll probably get someone to look at him as well.
“Jonathan will probably be assessed tomorrow when all players go and have a review of today.”
Biggar’s injury could be a complication for Gatland, with Rhys Patchell the only other specialist fly-half in the 31-man squad.
Asked who would be cover at number 10, Gatland replied: “I don’t know.”
“We’ll sit down as coaches and look at that.
“Some players are going to have to back-up, particularly backs. We may go for a 6-2 split on the bench with six forwards.
“We’ve been running Hallam Amos at 10 in training and he’s looked pretty sharp there.
“Gareth Davies went on the wing for us today and he did a job for us there.
“With the short turnaround, we need to freshen players up. Hopefully we’re good enough to do a job on Sunday to secure this group.”
Can’t see this selector? Visit this page
All pics via Huw Evans Images