Casillas took a kick to the hand after 18 minutes of the 1-1 draw, which safely saw Madrid through to the semi-finals with a 3-1 aggregate win.
A club statement on Thursday morning confirmed Casillas had a fracture.
"After carrying out initial x-rays at the La Moraleja Sanitas Hospital it has been confirmed that the footballer Iker Casillas has suffered a fracture at the base of the first metacarpal on his left hand," the statement read.
"It will be assessed again by a specialist later today to decide what treatment will be followed."
While no estimate was given on how long Casillas might be sidelined, an injury of this type could take up to three months to heal.
That will mean a return to duty for back-up Antonio Adan, who has been controversially picked by coach Jose Mourinho ahead of Casillas in a handful of recent matches.
Real face Manchester United in the Champions League last 16, with the first leg taking place in Madrid on February 13 before the return leg at Old Trafford on March 5.