Helen Bleazard’s AFC Bournemouth side were set to head to the Baggies’ Alexander Stadium on Sunday, but the match was called off due to weather conditions at the ground on Saturday afternoon.
The game will be rescheduled, with the winners of the tie set to face either Burnley or Plymouth Argyle in the final.
The Cherries said in a statement on their website that a new date for the fixture will be announced in due course.
Bournemouth defeated Swindon Town 3-0 in the quarterfinals to reach this stage, while West Brom beat Wolves 1-0 to reach the final four.