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."