Media named the suspect as soldier Ivan Lopez, 34, although his identity has not been officially confirmed.
Ivan Lopez took his own life with a .45-caliber Smith and Wesson semi-automatic pistol, officials say.
He had served in Iraq and had mental health problems, officials said.
President Barack Obama said he was “heartbroken” over the attack. A gun rampage at the same base in 2009 left thirteen soldiers dead and 32 wounded. Maj. Nidal Hasan was sentenced to death for that attack.
US military spokesman Lt Gen Mark Milley told reporters that there was so far no indication that Wednesday’s shootings were related to terrorism.
He said the suspect had not been injured when he served in Iraq in 2011, but was being assessed to see if he had post-traumatic stress disorder (PTSD).
The suspect was being treated for depression and anxiety, Mark Milley added.
The general said that it was not clear if the attack was premeditated and those wounded and killed were all members of the military.
The soldier drove to two buildings on the base and opened fire before he was stopped by military police, in an incident that lasted between 15 and 20 minutes.
He then shot himself in the head with a .45-calibre semi-automatic pistol. Officials say the weapon had been bought in a local store.
Barack Obama told reporters in Chicago: “I want to just assure all of us we are going to get to the bottom of exactly what happened.”
He said Ford Hood had sacrificed so much for freedom.
“We know these families. We know their incredible service to our country and the sacrifices that they make. Obviously our thoughts and prayers… are with the entire community,” the president said.
Defense Secretary Chuck Hagel called the shooting a “terrible tragedy.
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