Spain's number one was trying to collect a loose ball in the area early in the first half of the second leg match at the Mestalla when team mate Alvaro Arbeloa accidentally kicked the hand as he attempted a clearance.
Casillas was replaced by reserve keeper Antonio Adan and Jose Mourinho's side went on to secure a 1-1 draw that put them into the semi-finals 3-1 on aggregate to face Barcelona or Malaga, who meet later on Thursday.
"After carrying out initial X-rays... it has been confirmed that the footballer Iker Casillas has suffered a fracture at the base of the first metacarpal on his left hand," Real said in a statement on their website.
"It will be assessed again by a specialist later today to decide what treatment will be followed," they added.
As well as Sunday's game against Getafe, Casillas is also likely to miss next week's Cup semi-final first leg.
He is also a serious doubt for Real's Champions League last 16, first leg at home to Manchester United on February 13 and Spain's friendly against Uruguay on February 6.
"When I tried to close my fist it hurt. It's just the thumb. The fact that it has nothing to do with the wrist is good," Casillas, who had his left hand heavily bandaged, was quoted as saying on the club's website.
The injury to a key figure comes at a delicate time for Mourinho with Europe's elite club competition resuming in just over two weeks.
Casillas has just been restored to the starting line up after Mourinho controversially dropped him for the league games either side of La Liga's winter break.
The decision provoked angry reactions from home fans and fuelled media speculation about possible dressing room rifts even though Real's defence has started to tighten up of late.
The 2011 King's Cup winners will face a high-profile clash with great rivals Barca if the holders can beat Malaga in their quarter-final second leg at the Rosaleda.
The scores are level at 2-2 after Malaga snatched a late equaliser in last week's first leg at the Nou Camp.
SLOW TO REACT
Real have only conceded one goal in their last five outings in all competitions, while in their previous five they had conceded 12.
Adan was at fault for the goal conceded in Valencia on Wednesday, a low free kick he was slow to react to, but assistant coach Aitor Karanka defended him.
"Adan knows we have confidence in him," he said. "He played recently and was unlucky to get sent off. He knows he is young and has to progress, and that he has our backing."
The cup and the Champions League have taken on extra significance for Real who trail La Liga leaders Barca by 15 points, and second-placed Atletico Madrid by seven as their title defence has faltered.
"This season, where we aren't going to win the league, we have to think about the Champions League and Cup," Mourinho said in an interview with a French radio station on Wednesday.
Barca will be looking to put last weekend's first league defeat of the c
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