Morch joined Albion on a youth loan deal in mid-August to act as cover for Dean Lyness after on-loan Sunderland goalkeeper Jordan Pickford suffered an injury in training and had to go back to the Barclays Premier League club.
The Norwegian was an unused substitute on six occasions during his time at the Pirelli Stadium.
Pickford rejoined Burton on Friday and was restored to their starting line up the following day as they lost 2-1 at home to Portsmouth.
Morch, in his second year as a professional at Derby, is now expected to feature heavily for Rams' Under-21 side this season.
Manager Nigel Clough said: "We knew when Mats joined Burton on loan it was unlikely he would get game time for their first-team, but he's had the experience of being in a matchday squad for the first time and that was, no doubt, a great experience for him."
Meanwhile, another of Derby's young keepers has had his loan at Gresley extended.
Ross Etheridge joined Evo-Stik Northern Premier League Division One South side last month and, after impressing in his seven appearances to date, will now remain at the Moat Ground until November 16.
Etheridge, 18, signed his first professional contract in the summer after two years as a scholar at the Rams' academy.