Topley suffered a freak injury during a training drill in Brisbane on Monday before England's final warm-up match against Pakistan, rolling his ankle after stepping on a boundary cushion.
Scans have since revealed 'significant ligament damage' to the ankle with the team confirming on Wednesday he will play no part in the month-long main tournament.
It stands as a blow to England's World Cup hopes given the left-armer's strong form this year.
It is also desperately disappointing for Topley himself having already overcome a series of setbacks in the past, including a number of stress fractures to his back.
Fellow left-armer Tymal Mills has stepped up from his role as a travelling reserve to replace Topley, with Luke Wood to join the squad as a reserve.
England's first group game is against Afghanistan on Saturday before facing hosts and defending champions Australia, 2021 runners-up New Zealand and two qualifiers.
