The nine-times European champions reacted swiftly by signing their former keeper Diego Lopez from Sevilla as cover, the Andalusian club said.
"The operation has gone well," said Miguel Del Cerro, the doctor who carried out the surgery on Casillas.
"The recovery period is eight to 12 weeks," he said after having inserted two screws in the keeper's hand. "It is best to wait and not talk about time periods."
Spain's number one was injured during the Copa del Rey quarter-final second leg against Valencia on Wednesday when defender Alvaro Arbeloa accidentally kicked his hand while trying to clear the ball.
Jose Mourinho's side went on to win the tie 3-1 on aggregate, setting up a semi-final against arch rivals and holders Barcelona.
Casillas will also miss both legs of the Copa Clasico. The first game is on Wednesday and the return will be on February 26 or 27, ahead of the weekend La Liga meeting between Spain's two biggest clubs.
The keeper will also be unavailable to Spain coach Vicente del Bosque when the world and European champions play Uruguay in a friendly on February 6.
Lopez, 31, came up through the youth ranks at Real and was number two to Casillas in the first team for two seasons between 2005-07 before moving to Villarreal.
He was sold to Sevilla when Villarreal were relegated last season but has struggled to secure a place in the starting line-up.
Lopez will be valued for his Champions League and international experience, having been a member of the Spain squad on a number of occasions.
According to media reports he has agreed a three-and-a-half-year deal with Real for a transfer fee of around 3.5 million euros.
Mourinho surprisingly dropped Casillas for the league games either side of the mid-season break, a move which proved extremely unpopular among home fans. Reserve keeper Antonio Adan made two starts in his place.
In the second game Adan was sent off, Casillas was restored to the starting line up and since then Real have improved in defence.
The equaliser conceded by substitute Adan against Valencia on Wednesday was the first goal scored against Real in five matches.
The longer-than expected recovery time for Casillas adds to the problems facing Mourinho after a turbulent week when Angel Di Maria and Fabio Coentrao picked up suspensions which rule them out of the King's Cup first leg along with Sergio Ramos.
On Thursday, club president Florentino Perez took the unusual step of calling a news conference to deny a media report there was a rift between Mourinho and captains Casillas and Ramos.
With leaders Barcelona holding a seemingly unassailable 15-point lead over Real in La Liga, the former Chelsea and Inter Milan boss has targeted the King's Cup and the Champions League as his priorities.
Both those competitions depend on strong performances in the next five weeks to ensure their season does not end in failure.
Real host United in the Champions League on February 13 and visit Old Trafford on March 5.
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