Few details were immediately available about what led to the gunfire, but officials said the shooter was Quornelius Radford, 28, who used a personal handgun, not a military firearm.
Radford opened fire where he worked at the base in the state of Georgia, but officials wouldn't speculate about a motive, authorities said.
The injured soldiers are stable and expected to recover, said Brigadier General John Lubas.
The soldiers who tackled Radford helped ensure his arrest, Lubas said.
"These soldiers, without a doubt, prevented further casualties or wounded," he said.
This latest act of violence on a US military installation — sites that are supposed to be among the most secure in the country — again raised concerns about safety and security within the armed forces' own walls.
The Army said it's investigating the shooting.
The injured were treated and then moved to Winn Army Community Hospital, base officials said in a Facebook post, adding there's no threat to the community.
Some of the wounded were also taken to Memorial Health University Medical Centre in Savannah, said spokesperson Bryna Gordon.
Police were sent to the 2nd Armoured Brigade Combat Team complex shortly before 11am Wednesday. The shooter was arrested 35 minutes later.
The lockdown lasted about an hour.
Located about 64 kilometres southwest of Savannah, Fort Stewart is the largest Army post east of the Mississippi River.
It's home to thousands of soldiers assigned to the Army's 3rd Infantry Division and family members.
White House and Defence Department officials said President Donald Trump and Secretary Pete Hegseth had been briefed on the shooting.
Among the deadliest acts of violence on US military bases was a 2009 attack.
A US Army psychiatrist killed 13 people in a shooting that left more than 30 wounded at Fort Hood, a military installation in Texas.
In 2013, a defence contract worker and former Navy reservist killed 12 people at the Washington Navy Yard. He was then killed in a gun battle with police.
In 2014, a soldier opened fire on his fellow service members at Fort Hood, killing three people and wounding more than a dozen others before the gunman killed himself.
In 2019, an aviation student opened fire in a classroom at Naval Air Station Pensacola in Florida, killing three people and injuring another dozen people including two sheriff's deputies.
Just days earlier, a US Navy sailor shot two people to death before killing himself at Pearl Harbour, the Naval station in Hawaii.
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Catalini contributed from Trenton, New Jersey; and Associated Press writers Jeff Martin and Jeff Amy in Atlanta; Mike Balsamo, Konstantin Toropin and Mike Pesoli in Washington, D.C.; and Claudia Lauer in Philadelphia contributed to this report.
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