Morabito, who has already had two conventional knee reconstructions, tore the graft on his rebuilt knee at training last week.
He will have LARS surgery in Sydney next week.
Morabito, 21, has not played since his debut season, 2010, when he played 23 matches.
Fremantle's general manager football operations, Chris Bond, said it was important Morabito was given time to reach his decision.
"Anthony really just needed some time and space to weigh up his surgery options," he said on Wednesday.
"After discussions with people close to him and the football club, Anthony has decided that this surgery will give him the best chance to resume his playing career."
Bond said the club wasn't putting a time frame on a return date for Morabito.
"Obviously with LARS there's a shorter time frame with coming back, but we think he just needs to get back from the surgery and make sure that everything is OK first," he said.
"We'll see how he recovers from that and then we'll have a better idea."
