Monday's quarter-final draw also pitted league leaders Manchester City against Doncaster Rovers Belles, while in-form Birmingham City will host Liverpool.
London Bees, who knocked out Chelsea Ladies on penalties on Saturday, will travel to fellow-Women's Super League Two side Sheffield FC Ladies.
The ties will be played on 6-7 August.
Sheffield FC Ladies v London Bees
Birmingham City Ladies v Liverpool Ladies
Manchester City Women v Doncaster Rovers Belles
Arsenal Ladies v Notts County Ladies
Holders Arsenal Ladies will host Notts County in the Continental Cup quarter-finals, a repeat of the 2015 final and one of three all-top flight ties.