The Mexican great earned a dominant victory over his rival in the pair's trilogy fight at the weekend and did so despite tearing the cartilage in his left wrist beforehand.
Alvarez said: "It hurts everywhere. I had these issues since the Caleb Plant fight. I was like it's okay, it's okay, later, later, then it started [to get] really bad. I need surgery."
The super-middleweight world champion added: "With my hand problems I outjabbed the best jabber in the world in Gennadiy Golovkin.
"I think towards the end of the fight I obviously started to get a bit fatigued and that's because we've not been able to work explosively in the gym. But despite all the problems that we've had, I was really happy with my performance tonight.
"I wanted to get that KO but it didn't come because he's a great fighter. That's why there are 12 rounds in a fight. So you can show and display who's the best. So I'm really happy with what I've done tonight."
Canelo is now hoping to avenge his loss to Dmitry Bivol but concedes that he is unlikely to return to the ring until next year as he treats his injury.
The fighter said: "I'm going to take my time. My body needs [it]. Last year I fought four times in 11 months so that's why. I need to take my time a little bit maybe. May, September, I don't know. But I need to take my time."