The shooting happened in the town of Traiskirchen, 32 kilometers (20 miles) south of Vienna.
Austria News Agency quoted local police spokesman Johann Baumschlager as saying that the suspect fled in a vehicle and later took his own life.
The woman was flown to a hospital in Vienna. The Lower Austrian State Office of Criminal Investigation is investigating the shooting but could not immediately give any further details.
Local media reported that the shooting was preceded by an argument between the three people.
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