Nicknamed the Tongan Thor, tighthead Tupou has been one of Australia's best performers this season and had a major impact on the 35-15 Pool C win over Georgia last weekend.
He sat out training on Wednesday and the team said scans later in the day had confirmed the strain, but Broncan said he was still in the frame for selection.
"Yeah, Taniela has a minor injury but we are going to test him tomorrow, and for the game on Sunday," the Frenchman told reporters.
"I hope he'll be ready for the game against Fiji."
Zane Nonggorr (22) replaced Tupou for the last 10 minutes of the Georgia match in his fourth test and the other tighthead in the squad, Pone Faamausili (26), has also been struggling with a calf problem.
Australian media reports said coach Eddie Jones (63) was considering switching the experienced and versatile loosehead prop James Slipper (34) to the other side of the front row for the Fiji match.
Slipper is also recovering from an injury that ruled him out of Australia's opener at the Stade de France.
"Slipper and Pone were back training with team today, so no worries," Broncan added.
The Wallabies, who snapped a five-match losing streak against the Georgians, could all but secure a spot in the quarter-finals with a win on Sunday.
Fiji took Wales down to the wire in their opening Pool C defeat, however, and Broncan said Australia would need to be at their best.
"We need to play fast and pay with a lot of attention to the breakdown," he said.
"We are going to play against a very strong forward pack. We need to play a very good game to beat Fiji, it will be very tough."