The motive for the attack on Saturday is still under investigation, police said in a statement.
The Australian was arrested at the scene and the victim was taken to hospital.
Police declined to give further details on the identity of the victim and the alleged perpetrator.
Prosecutors could provide more information on Monday, a police spokesperson said.
Australian officials have reached out to authorities in Switzerland, a Department of Foreign Affairs and Trade spokeswoman said on Sunday.
"The Department of Foreign Affairs and Trade is aware of reports that an Australian has been detained in Switzerland and is making urgent inquiries with Swiss authorities," she said.
Stabbings have caused alarm in Europe in recent days, with an Algerian man arrested on Saturday in Mulhouse, France, over a deadly knife attack while a Syrian refugee was detained over a stabbing at Berlin's Holocaust memorial.
On Thursday, a teenage attacker killed two women with a knife in a shopping centre in the Czech city of Hradec Kralove.
A Syrian asylum seeker was arrested on February 15 on suspicion of going on a stabbing rampage in southern Austria.
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