Spurs, one of only two sides from below the Women's Super League left in this season's competition knocked out Brighton of WSL 2 on Sunday.
There will also be a Merseyside derby between Liverpool and Everton, plus two all-WSL 1 matches.
All the fifth-round ties are scheduled to be played on Sunday, 19 March.
Champions Manchester City will host fellow-top-flight side Reading, while Notts County host Yeovil in the other all-WSL 1 meeting.
Chelsea, winners in 2015, will be at home to WSL 2 side Doncaster Rovers Belles, while Birmingham City - who finished fourth in WSL 1 last term - will host West Midlands counterparts West Brom, who play in the third tier.
Notts County Ladies v Yeovil Town Ladies
Liverpool Ladies v Everton Ladies
Arsenal Ladies v Tottenham Hotspur Ladies
Sunderland Ladies v Aston Villa Ladies
Birmingham City Ladies v West Bromwich Albion Women
Bristol City Women v Millwall Lionesses
Manchester City Women v Reading Women
Chelsea Ladies v Doncaster Rovers Belles
Holders Arsenal Ladies will host Tottenham in the fifth round of the Women's FA Cup when top-flight sides enter at the last-16 stage.