The shootings occurred early Saturday outside a house in New Orleans, The (New Orleans) Times-Picayune reported.
The suspect, identified as Larry J. Haynes, 38, got into an argument with the victims and began shooting at them, then fled the scene, police allege.
Tiara Reynolds, 36, who was shot several times, was dead at the scene.
A 48-year-old man who was shot in the head was hospitalized in critical condition.
A 32-year-old woman who police said was the suspect's girlfriend, was shot in the arm, and another man had a gunshot wound to his body. Both were listed in stable condition.
Haynes is wanted on one count of first-degree murder and three counts of attempted first-degree murder.