Tupou was outstanding in Australia's 35-15 Pool C win over a physical Georgia side last weekend and would be a big loss for Sunday's match against the even more robust Pacific islanders.
"Taniela's sidelined, he's got a bit of a hamstring complaint, but we're just going to monitor him and then we'll just see how he goes over the next couple of days," said assistant coach Jason Ryles.
"He didn't train today but that's not unusual for Taniela, don't worry."
Experienced loosehead James Slipper was also running through his own programme as he continues to recover from a foot injury that ruled him out of Australia's opener at the Stade de France.
"I think he's certainly in the picture, but we're not exactly sure how that's going to pan out, whether it's this week or next week," said Ryles.
The win over Georgia snapped a five-match losing streak for the twice world champions this year and the mood in the camp was clearly upbeat.
Fiji showed in their narrow loss against Wales on Sunday that they are a side that needs to be taken very seriously and Ryles said the Wallabies were focusing a lot on defence this week.
If the Wales match is anything to go by, openside flanker Tom Hooper will have to get through a lot of tackling on Sunday and he said he had noted a marked improvement in the Fijians this year.
"They were always a team you sort of had to keep two scores on just in case they pulled something out of their clacker and went the full field," he said.
"But now, you saw on the weekend, it wasn't just miracle balls, it wasn't Hail Marys, it was really grafting and making those nice line breaks, consolidating that ball and then going on again.
"So they're a smart footy team now and they've got big athletes. So we're going to have to nullify that and defend really well."
