Livi defeated the Pars 1-0 at East End Park on Saturday to record their first SPL win of the season and leave the Fife club bottom of the table.
Livingston won the cup in 2004 and player-manager Paul Lambert said: "Celtic are the form team at the minute and are doing great, so I'm sure anyone would be glad to avoid them."
Dunfermline manager Jim Leishman added: "It's a great draw for both teams. Everyone wanted to avoid Celtic because they are the strongest team in the league.
"We want to give these boys something to fight for - the chance to get to a cup final"
Motherwell will play Celtic in the other Semi-final...