The Swans revealed the big setback in a Tuesday injury update on their co-captain, who had missed the last two games.
"Molloy has been experiencing back soreness in the last fortnight and following further investigation and specialist opinion, the club's medical staff have made the recommendation for Molloy to undergo surgery later this week," it said.
The Swans are ninth, outside the top eight on percentage, going into Saturday's home clash against 15th side Essendon. Sydney are on 24 points, along with seventh-placed West Coast, eighth side Adelaide and Fremantle, who are 10th.
The Swans will start strong favourites against the Bombers, but they will also need other results to go their way if they are to make their second finals series.
After winning their first four games this season, Sydney have dropped five of the last seven.
It is the latest significant setback for one of the AFLW's best players. Molloy missed most of last season with a knee reconstruction and had bounced back well in her return.
She also had back surgery after joining Sydney from Collingwood two years ago.
Molloy, 26, is a three-time All-Australian. She is equal fourth on the AFLW goalkicking this season with 19 in nine games, four behind leader Indy Tahau from Port Adelaide.
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