"A 38-year-old man shot several times at a 35-year-old woman and then shot himself," Zurich city police said in a statement, adding that according to their initial findings this was "a relationship crime".
The shots rang out around 2:30 pm outside a UBS bank branch just a stone's throw from Zurich's railway station.
Police said the exact circumstances surrounding the shooting were still being investigated.
In an earlier statement, police described how "rescue workers were dispatched and found one dead and one person badly injured, who later died of their injuries."
Police cordoned off a large area around the scene and insisted that the "situation is under control."
An AFP reporter on the scene saw around a dozen police vehicles and heavily-armed officers controlling the cordoned-off area.
Police did not provide any more details about the couple, but the Blick daily reported that they were both Italian nationals.
The paper also quoted a witness saying the couple had been at a nearby restaurant when they began a loud argument.
"They both went out into the street. There, the man shot the woman, and then turned the gun on himself," the unnamed witness was quoted as saying.
A picture published by the paper clearly showed a gun lying next to one of two covered bodies.
The 20Minuten daily also quoted a witness saying he had heard five shots ring out and had looked out the window of his classroom at a nearby school.
He said he had seen two people on the ground, one of them apparently holding a gun, the paper said.
On Saturday, Swiss media reported that the woman killed has been a UBS employee since 1998. The Blick published a copy of an internal memo from UBS Switzerland President Axel Lehmann expressing his condolences to the employee's friends and family.