Investigators still did not have a motive for the killings at the Louisiana Technical College in the state capital, Baton Rouge, police spokesman L'Jean McKneely told Reuters.
Details such as the names of the victims and the type of weapon used have not yet been released.
The early morning shooting came just hours after a gunman killed two police officers and three city officials on Thursday night when he stormed into a city council meeting in a suburb of St. Louis, Missouri. He was later shot dead by police.
Mass shootings are not particularly rare in the United States, where the gun-ownership lobby is politically influential and gun control is far less strict than in many countries.
In the worst shooting rampage in modern U.S. history, a student with a history of mental illness killed 32 people at Virginia Tech university in April 2007 before turning one of his guns on himself.
In December, a 19-year-old gunman in Omaha, Nebraska, killed eight people and then himself at a shopping mall. On Saturday, a man robbing a clothing store outside Chicago shot five women to death.