The 21-year-old will forgo the club's nine-day training camp in Darwin as a result.
Trengove will wear a protective boot, with club manager Josh Mahoney revealing the stress fracture had been detected in its early stages.
"This is clearly a disappointing setback for Jack. The positive element to this is that the stress fracture was identified early, which will allow Jack to begin his rehab immediately," Mahoney said.
"We expect Jack to be able to begin his running program in January. His rehab will be continually assessed but at this stage we are hopeful that he'll be available for the start of the AFL season."Trengove, who shares captaincy duties with Jack Grimes, became the youngest skipper in VFL/AFL history when he was appointed in February.