The details about the number of people hurt came from a senior U.S. defense official who spoke on condition of anonymity because the official was not authorized to discuss the information publicly.
Fort Hood's Directorate of Emergency Services said it had an initial report that the shooter was dead, but that the report was unconfirmed.
Earlier, Bell County Sheriff's Office Lt. Donnie Adams says the sheriff's office dispatched deputies and troopers from the Texas Department of Public Safety to the nearby Texas Army base.
Fort Hood ordered everyone at the base to "shelter in place." The order was sent Wednesday on the base's Twitter feed and posted on its Facebook page.
The 1st Calvary Division, which is based at Fort Hood, sent a Twitter alert telling people on base to close doors and stay away from windows.
The base was the scene of a mass shooting in 2009. Thirteen people were killed and more than 30 wounded.