Watson suffered the injury as he jumped with the Reds striker during the first half of Saturday's Premier League contest.
In a Tweet, Sterling wrote: "To Ben Watson I didn't realise it was serious as that. I'll be praying for a speedy recovery mate. I'll have you in my prayers every day."
The teenager was absolved of any blame for the freak injury by Wigan boss Roberto Martinez, who said after the game: "I haven't seen the challenge back, but I don't think any of the players were looking at each other.
"Both were looking at the ball - it's a real accident. It's a nasty collision.
"Ben has a fracture and we are going to assess him now because maybe he will require surgery. We will see what the extent of the breakage is and what treatment he needs.
"We are really disappointed because he was at a good level. We will keep our fingers crossed we can treat the breakage in a more conservative way."
Watson, 27, who has made 10 appearances for Wigan this season - scoring one goal - is expected to be out of action for four months.