Higuain went to Chicago to have surgery on a herniated disc and hopes to be playing again before the summer.
He told realmadrid.com: "I feel very relieved, which makes me a more positive person and more upbeat for what is to come. I don't know how long it will be before I am playing again, but I am happy and anxious to begin the recovery process.
"We must be cautious. I am young and have a lot of years of football ahead of me. I would be lying if I told you I didn't want to return as soon as possible.
"I am grateful to the club for all its help. I hope to return before season's end."
The 23-year-old was overwhelmed when his team-mates revealed they were wearing t-shirts bearing a message of support to him.
"I got emotional when I saw my team-mates walk onto the pitch with supportive t-shirts on. I sent them all a special message," he said.
"I am honoured as both a player and person. I am sure everything will turn out well."