Morphett will undergo surgery after fracturing her foot in their round-five loss to the Western Bulldogs, the Swans confirmed.
Overcoming a season-ending hand fracture last year, the All-Australian ruck was already managing the complaint when her foot was trodden on in the third quarter.
Morphett picked up the injury in the VFLW in August before being managed out of their round three and four clashes.
Sydney, sitting 11th with a 2-3 record after making finals last season, were already without captain Chloe Molloy (knee) when Morphett fractured her foot.
"Ally has worked incredibly hard to get herself back to optimum fitness this year, to see her go down like this is really disappointing for her," Swans coach Scott Gowans said.
"We were confident that through a reduced pre-season load and ongoing management she could play the majority of the season, but as we all know accidents happen in footy.
"The priority now is to get her body back to being fully fit so she can compete in the 2025 season and beyond."
Elsewhere, Geelong midfielder Amy McDonald has been sidelined for at least three weeks with a hamstring injury while forward Kate Surman is out with concussion.
GWS will also be without recruit Aliesha Newman for two to three weeks with knee soreness.
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