The incident occurred around 1pm in an underground parking area at the store in Dietlikon, a municipality northeast of the city of Zurich, cantonal police said.
The woman, a Swiss citizen, was taken to by ambulance hospital with serious gunshot wounds.
Her husband, an ethnic Albanian Serb, was transported separately by a Rega emergency rescue services helicopter to hospital where he died from his self-inflicted wounds, police said.
The couple’s three-year-old daughter, who witnessed the shootings, was not injured, police said.
She was taken into the custody of relatives.
The man was registered with cantonal police due to past cases of domestic violence, police said.
“I wanted to park and I saw him covered in blood and lying on the ground, trembling,” a witness told the Blick news site.
“I went to get help in the Toys’R’Us store,” the witness said.
“There a blond woman lay bleeding in the elevator on the floor.”
Police are investigating what led to the shootings.