Biggar lasted only 12 minutes of the Rugby World Cup Pool C match in Lyon, in which Wales became the first side to qualify for the quarter-finals.
“Dan’s got a stretched pec, we’re not too sure,” said Gatland.
“I haven’t spoken to the medics, but I spoke to Dan, they’re saying probably a couple of weeks.
“We’ve got 13 days before Georgia, so that potentially rules him out of that match. It’s not a significant injury.”
New Zealand-born Gareth Anscombe stepped into Biggar’s boots in impressive fashion, scoring 23 points as Wales racked up their highest ever points total against Australia, as well as their biggest winning margin against the Wallabies.
It was also Australia’s largest ever defeat at a World Cup.
“I thought it would be a close game,” said Gatland.
“We put a lot of work in in the last four months as a team together and we know that we’re a momentum team, we build on confidence in terms of performances.”
He hit out at critics who had downplayed Wales’s performances in the tournament so far: a 32-26 win over Fiji and 28-8 success against Portugal with a virtual B team.
“We saw yesterday (Saturday) Portugal are not a bad side, and considering the number of changes we made,” said Gatland.
“And I felt we didn’t get enough credit for the Fiji performance. Everyone was talking about how unlucky Fiji were, we kept that pretty much to ourselves.”
He added: “I thought today was an outstanding performance in terms of what we wanted to achieve and game management.”
Scrum-half Gareth Davies, one of Wales’s try-scorers, praised the impact that fellow veteran Anscombe had when he came onto the field.
“Dan Biggar going off was a shame but Gareth Anscombe has been training superbly and I was confident he would step in seamlessly, as he did,” he said.
Centre George North, another long-standing stalwart, said Davies had been instrumental in the victory, as he is at every World Cup for Wales.
“Every four years Gareth Davies seems to peak! It’s three months of graft and you get what you put in and we’re seeing that now,” said North.
“We were harsh on ourselves after Fiji and we’re not quite having those 80 minute performances yet. Still things to tidy up, but to do that to Australia is pretty good.”