A security guard patrolling the area found the young woman's body near Södra Station shortly after 2.30am.
"The circumstances at the scene indicate it was murder," said county police spokeswoman Kerstin Söderberg.
A police forensic examination at the scene did not provide any conclusive answers as to how the woman died. An autopsy will be preformed in order to determine the cause of death.
The 19-year-old woman was dropped off by a taxi at the crossing of Swedenborgsgatan and Fatbursgatan at around 10pm on Saturday.
"Before that she had been to a private party in Södermalm," said city police spokeswoman Petra Sjölander.
Sjölander could not say if the woman had shared the taxi with anybody else.
Police are currently working to track the woman's movements from the time she left the taxi.
So far there are no suspects and police are also considering the possibility that the woman might not have been murdered.
"It's possible to fall down from the pedestrian bridge, which is three or four metres high," said Sjölander.
Unless she was killed elsewhere and her body was dumped at the spot where she was found, the woman most likely died between 1.30am and 2.30am. The security guard who found the body had passed the same spot an hour earlier and was sure there had not been a body there at that time.
Police are seeking to make contact with witnesses who might have seen or heard anything potentially related to the woman's death.