Hashim Ajmal left HMP Sudbury, an open prison, on Tuesday.
The 22-year-old was convicted at Stafford Crown Court in 2019 for possession of heroin with intent to supply.
He has connections to the Dudley and Cradley Heath areas.
West Midlands Police has shared an appeal by Derbyshire Police urging people to call 101 if they spot him in the area.
A Derbyshire Police spokesman said: "Ajmal is an Asian male, 6ft tall and of slim build. He has brown eyes and brown hair.
"Ajmal has connections to the Dudley and Cradley Heath areas."
A West Midlands Police spokesman added: "Can you help Derbyshire Constabulary find Hashim Ajmal? He has links to the West Midlands and so may be in the area somewhere."
Anyone with information is urged to call Derbyshire Police on 101, quoting reference number 22 of November 24.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org