Slavia Prague reached the quarter-finals of the Europa League last season, where they were knocked out by Chelsea.
Celtic will have to overcome Cluj over two legs in order to face off against the Czech champions. The first leg takes place this coming Wednesday in Romania.
Neil Lennon's men easily defeated Nõmme Kalju 7-0 on aggregate in the previous round.
Slavia will be entered directly into qualifying at the play-off phase.