Police believe the spate of morning robberies in central Gothenburg and on the island of Hisingen were carried by two men on mopeds.
Many of the women were forced at knifepoint to hand over their handbags to the thieves, who set about their criminal work at around 6am on Saturday.
One woman received minor injuries when was stabbed in the hand outside Lundby Hospital at 7.15am, local newspaper Göteborgs-Posten reports.
Polcie said the man believed to be responsible for the Hisingen robberies rode a black moped, wore short trousers and a black jacket with red clothing underneath, and had a silver helmet, the newspaper reports.
Twice police came close to catching the thieves, who escaped by riding their mopeds onto bicycle tracks and footpaths.
Police have also confiscated a moped and some clothing in the city centre.
“I think we have a good chance of finding them. If any members of the public have seen anything in central Gothenburg or Hisingen, they can call the police’s tip-off line,” police spokesman Göran Andreasson told Göteborgs-Posten.
The number to call is 114 14.