Holders Manchester City have been drawn away to Newcastle in the FA Cup quarter-final draw.
City are aiming to win back-to-back FA Cup trophies for the first time in their history, while Newcastle are into the last eight of the competition for the first time since 2006.
Leicester's reward for beating Birmingham is a visit from Chelsea as third in the Premier League take on fourth.
Arsenal go to Sheffield United in what was the first tie pulled out of the hat.
Norwich will play the winners of Thursday night's remaining fifth round tie between Derby County and Manchester United.