The incident occurred around 10.30am in a hair salon in Wettingen, a town of 20,000 people.
Cantonal police said the man, aged 51, entered the salon and shot several bullets at the woman who died on the spot.
The attacker was seriously wounded by self-inflicted gunshot wounds.
He was transported by helicopter to the Zurich university hospital for treatment but he died shortly after noon.
Tagesanzeiger.ch, citing a neighbour, identified the man as the woman’s estranged husband, although this information could not be immediately confirmed by police.
Police did not initially identify the man or the woman. However, they did not rule out the possibility of a domestic dispute.
The shooting marked the final episode in a disagreement between the two Turkish immigrants, according to Tagesanzeiger.
The couple remained married but lived separately, while the woman had been the victim of several cases of wife battering, the news website reported.
The man had never been convicted of domestic violence but an investigation had been opened, police said.
The woman had just begun proceedings to secure a divorce.
The husband, a painter by profession, came to Switzerland from Turkey.
Many members of the local Kurdish community gathered at the scene of the crime on Wednesday afternoon.