City defeated Torquay United 2-0 on Wednesday to earn the trip to League One's bottom club. The Millers, deducted 10 points for going into administration, have a total of minus four points. A 3-1 victory over Oldham Athletic saw them through to the next round.
The match is due to be played the week commencing the 18th September. The two teams have not met since January 2004 in the Championship, when a 4-4 draw was the result. They met in the League Cup in 1989/90, with the Canaries securing a 3-1 aggregate victory.