It will be their first meetings since 2003/04, when both clubs were in the basement division.
"Fair credit to Scunthorpe, they've had a fantastic season," said Barmby.
"They'll be looking forward to playing in the Championship against the bigger clubs and the derby will be one of the highlights. It will also be good for us and our fans."
Humber derbies between Scunthorpe and Hull are notoriously tight - with the Iron just having the edge with 13 competitive wins compared to City's 12.