Police in Switzerland's Italian-speaking Ticino region said they had been alerted to a stabbing in a department store in the city of Lugano shortly before 2:00 pm (1300 GMT).
Initial investigations had established that a 28-year-old Swiss woman had attacked two other women, attempting to choke one with her hands, and injuring a second by cutting her neck with a knife.
Other shoppers managed to subdue the attacker, who was arrested, the police statement said.
An initial medical evaluation showed that one of the victims had suffered serious but not life-threatening injuries, while the other had minor injuries, police said.
Regional police said it did “not exclude terrorist motives”, adding that it was working with federal authorities and the local Lugano police on the case.