The tie will take place on the weekend of Saturday 21 March, with an exact date and time yet to be confirmed.
The draw, hosted by Mark Chapman and conducted by Martin Keown and Chris Waddle live on BBC One, also pitted holders Manchester City against Newcastle United at St James' Park, while Sheffield United take on Arsenal at Bramall Lane.
Leicester City will play Chelsea in the other tie.
THE FULL DRAW
Sheffield United v Arsenal
Newcastle United v Manchester City
Tottenham Hotspur/Norwich City v Derby County/UNITED
Leicester City v Chelsea
United were due to face Sheffield United at Old Trafford in the Premier League on Sunday 22 March.