The Sydney superstar was substituted out in the third term after injuring the finger in a tackle.
"It looks like he's broken his finger, so we'll see what the specialist says on Monday," said Sydney coach John Longmire.
"He's good, he's OK. He doesn't like missing footy, make no mistake about that, but after 18 years you understand that these things happen.
"He just went in for a tackle there and hit his finger. He'll be fine."
The 35-year-old Franklin had two goals to his name at the time but was forced to watch on as the Swans overran a determined Kangaroos outfit with the last four goals to claim an 11-point victory.
Franklin and the Swans were playing on the SCG for the first time since he set off wild crowd scenes when he kicked his 1000th career goal.
The eight-time Coleman Medallist has had his training program and playing loads monitored closely by the Swans since missing all of the 2020 season due to a series of soft tissue injuries but has so far avoided a repeat of those issues in 2022.
Swans veteran Sam Reid (one goal) moved well in his first game for the season and fellow forward-ruck Hayden McLean (two goals) was also a useful target against the Kangaroos.
Both Reid and McLean now loom as important players in the absence of Franklin, while Logan McDonald, the No.4 pick in the 2020 draft, is also likely to press his claims for a return to the senior team.
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