Last season's beaten finalists Villa face a tough trip to St Andrews and Manchester United will have to travel to Upton Park.
The quarter-final draw also pitted Arsenal against Premier League rivals Wigan at The Emirates and Championship outfit Ipswich at home to West Brom.
Ties will be played in the week commencing November 29.
Draw: Arsenal v Wigan, Birmingham v Aston Villa, West Ham v Manchester United, Ipswich v West Brom.
Source: Team Talk