A narrow defeat for the Canaries as a first half goal from Melkersen means pre-season ends with a 1-0 loss in Edinburgh.
City concluded their final pre-season fixture at Easter Road this afternoon, following part two of a double header in Scotland against Hibernian.
The Canaries started the match the livelier of the two sides, winning a corner inside two minutes.
Jonathan Rowe and Dimitris Giannoulis worked well on the left wing to allow the former to take a shot at six minutes in, which forced Hibs keeper Kevin Dabrowski to punch away to safety.
Elias Melkersen was on the end of the first promising attack for the home side as he charged goalward but before he can take an encouraging looking shot, he was flagged for offside.
Hibs then found their rhythm, putting Jonathan Tomkinson on alert in the box, but the centre back was able to close down a dangerous attack and see the ball out for a goal kick.
City's next promising attack came from the left wing again, when Giannoulis crossed into the box for Adam Idah, who was just out of reach to finish it off inside the six yard box.
Melkerson continued to trouble the Canaries, making another run at the City stopper, but isn;t brave enough to try to beat him to a ball in the box.
Just before 20 minutes, Onel Hernández made great use of his right wing and crossed into the box for Jordan Hugill, who was then denied by Dabrowski from close range.
City were then unable to get on the front foot again after plenty of Hibs possession, until after 25 minutes Jonathan Rowe went solo on the left wing and took a shot on the edge of the box. A Hibs shirt managed to prevent the shot hitting the target.
Just after the half an hour mark, the home side troubled the Canaries again after a scramble in the box allowed ex-City player Rocky Bushiri to take a shot at goal that was then flagged for offside.
City then fell behind at the 39 minute mark after Hibernian's number 20 capitalised on a miscalculation from Gunn and Melkersen's shot hit the roof of the net.
Minutes after the second half whistle, Hernandez managed a lovely run through the middle to cross nicely to Giannoulis, who was beaten by his defender but able to win a corner.
This then allowed the Cuban to take a shot on the edge of the area, but it was blocked and cleared to safety.
Hernández continued to keep pushing City forward as he worked hard to win a corner for the Yellows after the Canaries lost possession in an attacking position.
Just after the hour make, Hibs made a poor clearance following a Hernández shot, which allowed City to hold possession and fire at the target again, but with no real test for Dabrowski.
After 76 minutes, Krul was forced into his first real action since coming on, after a shot on target needed clearing from safety.
Ten minutes before time, the Hibs number nine Christian Doidge was given space in the box to shoot from an angle, but Krul was unphased as his shot soared wide of the target.
Hibs then won a free kick on the edge of the box after a late challenge, but were unable to finish off the cross into the box.
Five minutes before time, Hibs had the chance to make it two with a one on one with Krul in the box but couldn't find the target behind the City stopper.
City had one final spell before the whistle as Teemu Pukki's shot deflected to Sam Mccallum on the edge of the box, but the loan returnee was unable to fire past the Hibs defence.
Hibernian: Dabrowski, Miller, Porteous (McGregor 46), Kenneh (MacIntyre 46), Tavares (Blaney 46), Newell (Tait 46), Henderson (Doidge, 46), Melkersen (McCelland 46), Campbell (Delferriere 46), Bushiri (Bojang 46), McGeady (Hamilton 46)
Subs not used: Johnson, Hauge
Goals:
Norwich City: Gunn (Krul 60), Shipley, Tomkinson, Hills (McCallum 89), Giannoulis (Riley 60), Sørensen (Kamara 60), Gibbs, Rowe (McLean 82), Hernández, Idah (Pukki 76), Hugill (Sargent 82)
Subs not used: McGovern, Aarons
HT: 1-0
Venue: Easter Road