Victory saw the Canaries move up into sixth place in English football's second-tier Championship, five points behind Cardiff City who currently occupy the second and last of the two automatic promotion places on offer to the lucrative Premier League.
Maddison broke the deadlock just before the hour mark with a well-struck curling shot as Norwich remained unbeaten in derby matches since 2009.
It might have been a different story, however, if Ipswich's Jonas Knudsen, who hit the woodwork, or David McGoldrick, whose header from close range went over the crossbar, had managed to convert either of the hosts' most promising first-half chances.
Norwich's success gave manager Daniel Farke victory in his first East Anglian derby and took his side into the play-off places.