The 39-year-old has recently been getting involved in MMA during his spare time.
He was training for an official fight, but has now had to push back the date due to his injury.
On Facebook, Zuckerberg wrote: "Tore my ACL sparring and just got out of surgery to replace it. Grateful for the doctors and team taking care of me. I was training for a competitive MMA fight early next year, but now that's delayed a bit. Still looking forward to it after I recover."
The discussion came about after Musk tweeted in June that he "would be up for a cage fight" with the Facebook founder. Zuckerberg responded with "send me the location".
Zuckerberg's Meta launched Threads in July as a rival to Twitter, which has faced criticism since Musk's takeover.
The same day it launched, Musk threatened to sue over claims it was a "copy-cat app".
"Twitter has serious concerns that Meta Platforms has engaged in systematic, willful, and unlawful misappropriation of Twitter's trade secrets and other intellectual property," Twitter lawyer Alex Spiro wrote in a 'cease-and-desist' letter.
Musk also tweeted: "Threads is just Instagram minus pics, which makes no sense, given that thirst pics are the main reason people use that app.
"How many times have you read comments on Insta pics & wished there were more? Personally, never."
Despite the back and forth between the two billionaires, no date was ever announced publicly.