Police patrols have been stepped up and detectives are appealing for witnesses following two assaults on two women.
The women were both dragged to the ground by men in Collegiate Crescent, off Ecclesall Road, at around 8.30am on Saturday.
Both incidents occurred within minutes of one another and police believe they were linked.
The attacker ran off on both occasions after his victims shouted for help.
Detective Inspector Richard Partridge, leading the investigation, said: “I am seriously concerned about the actions of this man and the risk that he poses.
“We believe these assaults have a sexual motive, so we’ve increased the visible policing presence to reassure the local community.
“While thankfully neither woman was seriously hurt, we are urging anyone with information to come forward.”
The suspect is black, possibly aged in his 20s and was wearing dark clothing.
A 34-year-old man has been arrested and bailed.