On 3 August 2015, Norwich announced that Mulumbu suffered a broken metatarsal in a friendly against Brentford which would require surgery and sideline him for several weeks, ruling him out of the start of the season. He would finally make his debut on 27 October in a League Cup game against Everton, which Norwich lost on penalties after a 1–1 draw. He made his Premier League debut a few days later on 31 October in a 2–1 defeat to Manchester City. However, with Jonny Howson, Alexander Tettey and Graham Dorrans preferred in the centre of midfield, Mulumbu would ultimately be confined to only five league starts and two appearances as a substitute in the 2015–16 season, plus one appearance in the FA Cup, and the season would end with Norwich relegated back to the Championship.