The Brazilian midfielder was left in agony after a reckless tackle from Boro defender Emanuel Pogatetz took him out in the second half of United's 3-1 Carling Cup third round win at Old Trafford.
But a club spokesperson told United's official website on Wednesday morning: "We can confirm that Rodrigo did not suffer a break to his right leg. He was kept in hospital overnight for observation and to assess whether there was any ligament damage to his knee."
Reds boss Sir Alex Ferguson was not happy with the challenge, but later praised Middlesbrough manager Gareth Southgate for his apology after the game.
He said: "For the kid to make his first start and get an injury like that is pretty horrendous. I think everyone was numb for about ten minutes afterwards and it killed our momentum a little bit. I saw a few replays of it, but I don't want to see it again. It was just terrible.
"One of the guys on their bench was screaming that it was never a sending off and there was nothing wrong with Rodrigo. Middlesbrough have apologised though. Gareth Southgate was very good. He understood the gravity of it and was very apologetic."