Dinnington teenager Leonne Weeks was reported missing on Monday.
Friends and family posted desperate Facebook appeals for her whereabouts after she failed to return home.
Police said just 20 minutes after the missing persons report was received a body was discovered by a member of the public in a lane off Lordens Hill in Dinnington at 10.55am on Monday.
Later that day detectives arrested an 18-year-old Dinnington man on suspicion of murder.
At a news conference on Monday night, temporary superintendent Sarah Poolman said police were treating the death as suspicious because of "concerns around the state of the body and injuries."
Speaking at the scene on Tuesday, Leonne's relatives told how the girl's mum Paula and the rest of the family are "devastated and shocked."
Detective chief inspector Martin Tate briefed the media on Tuesday and said the investigation was in its 'early stages' and the formal identification process was not yet complete.
Police are still appealing for information in relation to the incident. Contact police on 101 quoting incident number 256 of 16 January 2017.