Trengove, who was dropped back to the VFL after Round 2, reported soreness in his foot after playing in Casey Scorpions' loss to Geelong on Sunday.
Scans on Monday revealed a crack on his navicular bone and he will undergo surgery on Wednesday.
It is devastating news for the club, who were rocked by the sudden retirement of Mitch Clark last week.
"Jack's attitude has been outstanding this year, particularly in recent weeks whilst playing in the VFL – and for this to happen to him is really unfortunate," Manager of football operations Josh Mahoney said.
"He is a resilient character. At Melbourne, we've had two examples of players who have had this type of injury in Colin Garland and Jack Grimes and they both made full recoveries. We expect Jack to make a full recovery, and be available for day one of pre-season training."
It is the second time the former co-captain has suffered a serious foot injury after he suffered stress fractures in December 2012.