Calvin Joseph Coleman, 22, was arrested about an hour after the shootings, said Assistant Police Chief Chris Stanfield. Police said he had registered at Louisiana Technical College, but had not attended classes for several weeks.
The shooting happened at about 11:30 a.m. in an electronics class at the vocational-technical school's Natchitoches campus, Stanfield said. Three students and an instructor were in the room at the time, police said.
"He came into the classroom and fired four or five times," Stanfield said.
Police Chief Ralph Peters said after the shootings the gunman jumped into a car and left with someone who had been waiting for him. Police would not say if the other person had been arrested.
The dead man was identified as Terome Silvie, 32.
The wounded man was identified as John Richardson, who was taken to Natchitoches Parish Hospital for treatment of a leg wound described by Peters as minor.
Peters said the shootings did not appear to be random and investigators believe Silvie was the intended target. Richardson appeared to be an innocent bystander, Peters said.
Police were not sure of a motive, Stanfield said.
Peters said the gunman was apparently not signed up for the class where the shooting took place.
Classes were canceled for the day after the shooting. The school is one of 42 two-year schools in the state system of trade schools. In addition to associate degrees, the school also offers diplomas in skilled trades.
Natchitoches is in northwestern Louisiana, about 60 miles southeast of Shreveport.