Trengove, Melbourne's co-captain for 2012 with Jack Grimes, will not travel with the team to the club's nine-day training camp in Darwin.
However, the Demons remain hopeful the 22-year-old will be fit for their 2013 season opener against Port Adelaide.
Melbourne football manager Josh Mahoney said the stress fracture had been identified early, allowing Trengove to begin his rehab immediately. ?
"This is clearly a disappointing setback for Jack," 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."