The Aviva Premiership rivals were due to face off at the Kingsholm Stadium in Gloucester at 3pm, only for overnight snow to cause the cancellation of the fixture.
A decision to postpone the match was made by organisers this morning, with a new date yet to be set.
"Today's Anglo-Welsh Cup Final has been called off, due to the adverse weather conditions," a statement read. "The decision has been made with the safety of supporters, players and officials in mind. An announcement about a new date and arrangements for ticket holders will be made in due course."
Exeter currently lead the way at the top of the Aviva Premiership standings, sitting 15 points ahead of sixth-placed Bath.