Base commander Lt Gen Bob Cone said that the gunman had not been killed, as earlier stated, but was in custody.
Major Nidal Malik Hasan identified as the gunman
Two other suspects were questioned, but the army now says only one gunman was involved in the incident.
Lt Gen Cone said the motive for the shooting was not known. One of the dead was a policeman, others were soldiers.
President Barack Obama described it as "a horrific outburst of violence".
Speaking at a press conference in Washington, he said: "It is difficult enough when we lose these brave men and women abroad, but it is horrifying that they should come under fire at an army base on US soil."
He extended his condolences to the families of the victims, adding: "We will make sure that we get answers to every single question about this horrible incident."
The gunman has been named as Major Nidal Malik Hasan. He is now said to be wounded after being shot a number of times, but in a stable condition in custody.
"His death is not imminent," said Lt Gen Cone.
Maj Hasan, aged 39, was a military psychiatrist and was reportedly due to be sent on a mission to Iraq.
His cousin said Maj Hasan - a US-born Muslim - had been resisting such a deployment.
"He hired a military attorney to try to have the issue resolved, pay back the government, to get out of the military. He was at the end of trying everything," Nader Hasan told Fox News.
He also said that Nidal Malik Hasan had been battling racial harassment because of his "Middle Eastern ethnicity".
Prior to Fort Hood, Maj Hasan served as a psychiatrist at the Walter Reed Army Medical Center in Washington, which treats wounded troops from combat zones.
The shooting had begun at about 1330 (1930 GMT) on Thursday at a personnel and medical centre at Fort Hood, where soldiers who are preparing to deploy go for last-minute medical check-ups, Lt Gen Cone said.
He said the gunman had two weapons, one semi-automatic, which "might explain the rate of fire".
Asked whether the shootings were a terrorist act, Lt Gen Cone said: "I couldn't rule that out but I'm telling you that right now, the evidence does not suggest that."
Two more suspects were apprehended in an adjacent facility, he said, but eyewitness accounts suggesting there might have been more than one gunman were later discounted.
A serviceman stationed at Fort Hood who asked to remain anonymous told the BBC: "I heard the emergency announcement over the speakers outside and saw people rushing to get indoors."
Local congressman John Carter, speaking to NBC News, said gunfire had erupted half an hour before a graduation ceremony was due to begin.
News Sourse: BBC News