Rain had fallen all day in Dundee and left parts of the Dens Park pitch waterlogged.
Dark Blues boss Gary Bowyer said: “When we walked on the pitch, there were areas that were unplayable. The ball didn’t bounce when the referee threw it.
“I feel for the supporters – and especially the Dunfermline supporters that were travelling but he gave it as long as he possibly could.”
Now they will try it all again as Bowyer takes on former Dens boss James McPake for a place in the last four of the competition.
The two managers will take their places in the dugouts next week after the match was rescheduled.
The game will now be played on Tuesday, January 17 with a 7.45pm kick-off.
BBC Alba, however, will not be broadcasting the tie live on television, as was the case for the original game.