The incident took place at the historic hotel, located in The Crescent, at around 5am on Saturday, April 16.
A man entered the hotel and threatened a member of staff before making off with cash in the direction of The Slopes.
Derbyshire police say nobody was hurt in the incident but the staff member was left shaken.
The suspect was described as white, in his 50s, of chubby build, and was wearing dark clothing including a black hoodie.
Detectives investigating the robbery are now asking for anyone with information to come forward.
Witnesses, or anyone with information or relevant CCTV footage, should call Derbyshire police on 101 quoting reference 22*215064.
To report information anonymously, contact Crimestoppers on 0800 555 111 or visit the Crimestoppers website.