More than 50,000 messages of support have been left for the Wales youngster, whose season was ended following a tackle by Stoke defender Ryan Shawcross which left the 19-year-old with a fractured tibia and fibula.
"I am very sorry for him because he is such a young and talented player," Gilberto told the club's official website, arsenal.com.
"I hope he is patient because it is not going to be easy. I had a back problem a few years ago and the best way is to be patient and be with your family.
"It is the kind of thing you cannot change so only do the rehabilitation with the physio when you are able to."
Gilberto added: "He does not have to rush and has time because he is only 19.
"It is very important for him to have a good recovery. If he rushes himself to be back too quickly, maybe he will have a setback in his recovery. He needs to be strong, especially mentally.
"He must not think 'I am young and I have this injury' because he will be back.
"He just needs to be patient and stay positive."