The operation was a success, but the 25-year-old Spanish striker was immediately ruled out of Wednesday's Champions League quarter-final second leg away to Manchester United as the club estimated that he would need a month to recover.
"Raul has successfully undergone surgery for appendicitis at the Ruber clinic [in Madrid]," Real said in a statement. "He will stay in under observation overnight and it is hoped that he could return home on Tuesday.
"He will be able to return to training within seven to 10 days and it is estimated that in 30 days he could be available again to coach Vicente del Bosque."
Raul scored twice in Real's 3-1 win over Manchester United in the opening leg of their Champions League quarter-final and he had been due to lead the line in the return at Old Trafford on Wednesday.
United manager Alex Ferguson, who named him the world's best player after that performance, will be mighty relieved to see the Spaniard absent from the Real line-up on Wednesday.
Raul's absence will also be felt in the Spanish league, with Real holding a one-point
The most pressing concern will be in the Champions League, however, with Raul set to miss not only Wednesday's game against Manchester United but also both legs of a possible semi-final against Juventus or Barcelona.
"We're professionals and we can't start crying about it," del Bosque said after learning he would not be able to include Raul in his squad. "He's a notable absence and he gives a lot to this team, but the squad is strong enough to do the job at Old Trafford.
"We'll just hope that he gets better as soon as possible."
Captain Fernando Hierro said the squad would look to dedicate a victory over United to their team mate.
"It's a real blow," he said, "but as a footballer, there are always things happening that you can do nothing about. The important thing is that he recovers and that we beat Manchester United so that we can dedicate victory to a friend and team mate."
