The Hammers face a difficult task if they are to advance to Wembley after they were paired against arguably the strongest team left in the competition.
Manchester United overcame Wolves in the last round whilst the Hammers had to go to extra time to beat Stoke City.
The quarter final tie will take place at the Boleyn Ground on the week commencing 29th November.
The draw in full:
Arsenal v Wigan
Birmingham v Aston Villa
West Ham v Man Utd
Ipswich Town v West Brom