19-year-old Mario Garza was one of two men who opened fire in the parking lot of the Walmart store on East Franklin Road, police say.
The shooting occured at about 10:15 p.m., as people were gathering in the lot to watch the fireworks show from the nearby God and Country Family Festival.
Investigators say that Garza and 21-year-old Ezri Garcia had an argument that led to a fistfight before both men pulled out guns and stated shooting at each other.
A bullet hit a 10-year-old girl in the shoulder. Police say the child was there with her family to watch the fireworks, and did not know either suspect.
The girl was rushed to a local hospital for surgery, but her injuries are not believed to be life-threatening.
Garcia was arrested on the spot, but Garza is on the run.
Garza is described as a Hispanic man with brown hair and brown eyes, 5'11'' and weighing about 150 pounds. He is said to be of a slender build.
A warrant has been issued for Garza's arrest on charges of aggravated assault with a gang enhancement and rioting.
Anyone who spots Garza or has information on his whereabouts is asked to contact the Nampa Police Department at 465-2257.