The women apparently were shot in their seats in the second-floor classroom at Louisiana Technical College, Baton Rouge Sgt. Don Kelly said. About 20 people were in the room at the time, he said.
Officers ran into the building within four minutes of the first 911 call, which came at 8:36 a.m., Kelly said.
"There was mass pandemonium, people running," he said. "One officer - the first into the classroom - told me he could still smell gunpowder."
One of the victims, 27-year-old Taneisha Butler, was a mother of three. Her husband, who arrived on the scene, told Anna Adair of CBS affiliate WAFB that his wife was a nursing student. The couple's three children are 4, 9, and 12 years old.
The school - one of two LTC campuses in Baton Rouge and dozens around the state - offers classes in a dozen subjects including early childhood education, practical nursing, drafting and welding.
School administrators and campus police did not immediately return calls or e-mails.
Louis Davis, who said he was taking an automobile technology class Friday morning, said a teacher told the students to stay in class because there had been an incident, without adding details. Students had to stay in their classrooms for about two hours and were briefly questioned by police before being released for the day, he said.
Classes were canceled through Tuesday, and tentatively scheduled to resume Wednesday, said Jim Henderson, vice president of the Louisiana Community and Technical College System.
"This is a tragic day for Baton Rouge, when you come to a learning institution ... and become the victim of a violent crime," Mayor Kip Holden said at the scene.
Meanwhile, in Greenville, S.C., a student was shot in the leg at Greenville Technical College, but told police it was a self-inflicted accident, a campus official said. The wound was not life-threatening, said Brad Majors, the college marketing director. Majors said campus police and city police would continue to investigate.