Monday’s draw happened live on BBC Radio 1Xtra, with Women’s Super League and Championship sides entering.
Crawley are just one of three teams from the fourth grade still staying, combined with AFC Wimbledon and Keynsham Town.
The ties will be played on Sunday, 3 February, with each winning side receiving £2,000 in prize money.
All 2-2 clubs from the major two tiers input the contest at the fourth-round point, joining the lower-ranked 10 sides who progressed from Sunday’s third-round ties.
The Gunners will visit a Crawley side who are high in the fourth largest tier’s South East region, with won each of nine of their league matches to date this term.
Crawley’s league rivals AFC Wimbledon will also host top flight resistance in Bristol City, while Keynsham are off to WSL team Reading.
This year’s final is going to be held in Wembley on Saturday, 4 May.
Fourth-round draw in complete
Loughborough Foxes v Sheffield United
Charlton Athletic v Huddersfield Town
Manchester City v Watford
Yeovil Town v Birmingham City
AFC Wimbledon v Bristol City
Millwall Lionesses v Lewes
Durham v Cardiff City
Crawley Wasps v Arsenal
Leicester City v London Bees
Reading v Keynsham Town
Liverpool v Milton Keynes Dons