The all-rounder, who was due to join the Club for the entire Vitality Blast and the final seven Specsavers County Championship matches, will undergo surgery and will be out of cricket for six to nine months.
The Club are now reviewing its options for an overseas replacement, led by Cricket Advisor Kim Barnett, Specialist Twenty20 Coach John Wright and Club Captain Billy Godleman.
Barnett said: “It’s desperately disappointing for Mitch, who I know was looking forward to his stint in England with Derbyshire this summer. But he must put his long-term future first.
“We are already reviewing our options for potential overseas replacements, working with John [Wright] and Billy [Godleman]. There are several options available to us.
“We have already secured our overseas for the first half of 2018 in South Africa international Duanne Olivier, who will provide an added quality seam option for the first seven four-day games and the entire Royal London One-Day Cup.
“Meanwhile, it’s great that John and Dominic Cork will also be back for the Vitality Blast, providing vast experience and a strategic lead for the competition as we look to progress further following last summer’s record-breaking campaign.”