The shots rang out around 2:30 pm outside a UBS bank branch just a stone's throw from Zurich's railway station.
"Rescue workers were dispatched and found one dead and one person badly injured, who later died of their injuries," Zurich city police said in a statement.
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 details but appeared to have concluded there was no outside shooter.
"We are not searching for anyone," police spokesman Christian Spaltenstein told AFP.
The Blick daily meanwhile quoted a witness saying those involved had been a couple who 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.
The paper published a picture clearly showing a gun lying next to one of two covered bodies.
The 20 Minuten 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.
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