The Louisiana police officer was fatally shot Wednesday afternoon, authorities said.
One of the women who was stabbed also died, Deputy Sheriff Paul DiCapo of the St. Landry Parish Sheriff's Office said.
Two other women were hospitalized, according to CNN.
The suspect, 35-year-old Harrison Lee Riley, was hospitalized after fleeing in his car from the house in Sunset, Louisiana, where the incident occurred. He crashed into a convenience store several blocks away, police said.
Riley barricaded himself behind an office door but gave up after police used tear gas and broke into the room.
DiCapo identified the officer as Henry Nelson, 52. Shameka Johnson, 41, died of her stab wounds. Her sister Surlay Johnson, 34, is in serious condition.
They are sisters of the mayor of nearby Grand Coteau, Shaterral Johnson.
The third woman -- Courtney Jolivette Riley, the suspect's wife -- was in stable condition.
The suspect had some irritation to his eyes from tear gas. He was unhurt otherwise.
Sunset is a town of about 3,000 people located some 15 miles north of Lafayette, Louisiana.