The revised diagnosis means the England captain could still make the latter stages of the World Cup if his recovery goes well.
"This is a real blow for David personally, for Manchester United and for England," admitted England manager Sven-Goran Eriksson.
"But there is nothing we can do about it.
"I am sure that the medical staff at Manchester United will be doing everything in their power to ensure that David recovers fully and quickly," he added on the FA's official website.
FA chief executive Adam Crozier said he was hopeful Beckham would make the finals in June.
"Clearly the first 48 hours are always crucial, but it sounds a little bit better and hopefully things will improve," he said.
The 26-year-old midfielder will however definitely miss the rest of United's domestic and European campaign.
He was injured by a tackle from Deportivo's Pedro Duscher during United's 3-2 victory on Tuesday night.
And according to his father, Beckham is "devastated" by the injury that threatens to wreck his season.
Ted Beckham said: "David called me from hospital to let me know how he was.
"To be honest he was devastated.
"He was very, very upset and he said he was in a lot of pain and that he was in plaster.
"He said he was more upset because of what games were coming up," he told GMTV.
"I really feel sorry for him. It's a terrible thing to have happened. But, fingers crossed, he'll be OK."
Beckham was driven from his flat on Thursday morning by team-mate Dwight Yorke to begin his rehabilitation at Old Trafford.
Wearing a woolly hat, the England star held his hand up to his face and looked away from reporters and photographers. He also had crutches next to him in the car.
Manchester United boss Sir Alex Ferguson had said of his star player after the match: "The Champions League quarter-finals have been an unfortunate round for him, but he's young and there will be other campaigns.
"You could see the pain he was in, but he will play in the World Cup again and he will play in the European Cup again."
Ferguson would not condemn Duscher's tackle, instead adding: "The game of football is about tackles and I think the player maybe had to go for it (the ball)."
Deportivo coach Javier Irureta insisted he had not sent his players out to injure Beckham.
"We didn't single Beckham out for special treatment," he said.
"I hope he recovers from it quickly and I feel sorry for what has happened."