The 35-year-old man was walking along Fratton Road at around 10.45pm on Sunday (January 31), when a group of youths asked him to buy them cigarettes.
When he refused one of the males in the group punched him in the face causing the victim to drop his bag.
The offender grabbed the bag and run off down Garnier Street, leading into Murefield Road and onto Arudle Street.
The bag contained a white Husban Mini Drone in a box, which had four propellers and a fitted camera.
The robber is described as being:
In his late teens to early 20s
Between 5ft 8ins and 5ft 11ins tall
Of a slim build
He was wearing a black coloured beanie style hat, a dark hooded jacket, dark tracksuit trousers and had a bicycle prior to the assault.
The victim suffered minor injuries to his face but did not need hospital treatment.
Detective Constable Samantha Hockley said: “The male offender was with a group of youths prior to the incident and some of those witnessed the robbery, so we are urging them to come forward and speak to us.
“We would also like to hear from any businesses who have been offered a drone for sale since this incident and from any residents in the area who noticed anything suspicious at the time of the assault.
“The item stolen is slightly unusual so people might have information about where it is.”