Mr Musk, who turns 52 later this month, also tweeted: "I have this great move that I call "The Walrus", where I just lie on top of my opponent & do nothing."
He also tweeted: "I almost never work out, except for picking up my kids & throwing them in the air."
Meanwhile, 39-year-old Mr Zuckerberg has already been training in mixed martial arts (MMA) and has recently won jiu-jitsu tournaments.
I wish Elon follows his big mouth and gets punched hard