Albion will face Nottingham Forest at home in the fourth round of the Adobe Women's FA Cup.
The match will take place at Broadfield Stadium on Sunday 18 January, kick-off 1pm.
Ticket information will be confirmed in due course.
The full draw is as follows:
Charlton Athletic v Swindon Town
AFC Bournemouth v Manchester City
Ipswich Town v Sheffield United
Oxford United v Middlesbrough
Chatham Town v York City
Arsenal v Aston Villa
Manchester United v Burnley
Southampton v Bristol City
London Bees v Liverpool
Tottenham Hotspur v Leicester City
Brighton & Hove Albion v Nottingham Forest
Chelsea v Crystal Palace
Newcastle United v West Ham United
Sunderland v London City Lionesses
West Bromwich Albion v Everton
Hull City v Birmingham City