The Cleveland Browns star wide receiver will miss the rest of the season after limping off during the Oct. 25 divisional matchup against the Cincinnati Bengals. Beckham has played only 39 out of 64 games over the past four seasons because of injuries.
Beckham was a guest of Hamilton's at last year's Monaco Grand Prix, which the Mercedes driver won. Hamilton, who is inching closer to a record-equalling seventh world championship and at last weekend's Portuguese Grand Prix won a record 92nd race, has backed his friend to make a full recovery.
"I haven't spoken to him; I messaged him the other day about his injury, but as you can imagine when you go through something like this, he's probably having some time focusing on healing and probably receiving a lot of messages," Hamilton said. "I know at some point we'll connect.
"He's an incredible talent, and he's still young [Beckham will turn 28 next week], I think he's got such a bright future. What he's done already with his new team has been impressive.
"I think what's really, really important -- and I've not done my ACL before -- but what I think I know about recovering is to never rush those things, just focus on healing so you can be even stronger. He's already a machine. Those athletes are absolutely incredible, so I'm sure he'll have the best advice and help in terms of recovering.
"But I don't know what the next steps are for him in terms of becoming the great that I know that he can be. That's his journey, and I know that he'll know what he needs to do to do that."