The Netherlands international has not played a La Liga game this season but has been the team's first-choice goalkeeper in the Copa del Rey in his three seasons at the club, lifting the trophy in 2017 and 2018.
He made a vital contribution to Barca's win over Sevilla in Wednesday's quarter-final second leg, saving a penalty from Ever Banega which, had the Argentine scored from, would have seen Sevilla take a 3-1 aggregate lead in the tie.
Barca went on to win the game 6-1 for a 6-3 aggregate victory.
German international Marc-Andre ter Stegen is set to stand in for Cillessen in Barca's semi-final first leg against Madrid on Feb. 6 and the second leg on Feb. 27 or 28.
If Barca progress from the tie, Cillessen would be expected to return to play the final against Real Betis or Valencia on May 25.
(Reporting by Richard Martin, editing by Ed Osmond)
