The suspect was identified as Adam Alsahli of Corpus Christi, according to three officials familiar with the investigation who were not authorised to speak publicly and spoke to The Associated Press on condition of anonymity.
At about 6.15am on Thursday, the gunman tried to speed through a security gate at Naval Air Station Corpus Christi, opening fire and wounding the sailor who was a member of base security, US officials told the AP.
But she was able to roll over and hit the switch that raised a barrier, preventing the man from getting onto the base, the officials said.
Other security personnel shot and killed the man.
There was an initial concern that he may have an explosive device, but Navy experts swept the area and the car and found nothing.
Later on Thursday, federal agents were seen carrying items from inside a house that a Corpus Christi police tactical unit had surrounded and a public records search by local television station KRIS indicated was Alsahli's last known address.
FBI Supervisory Senior Resident Agent Leah Greeves said at a news conference that investigators were working to determine whether a second person of interest was at large but did not elaborate.
She also would not discuss a potential motive or specify what led investigators to believe the shooting was related to terrorism.
"We are working diligently with our state, local and federal partners on this investigation, which is fluid and evolving," Greeves said.
The FBI's field office in Houston has taken the lead on the investigation, and neither investigators nor the Navy provided details on the shooter or a possible motive.
The injured sailor was discharged from a hospital where she was treated for minor injuries, according to a statement from the command.
The air station is surrounded by water on three sides and is home to Naval pilot training since 1941, according to its website.
Marine Corps, Navy and US Coast Guard student pilots train there. It's also home to the Corpus Christi Army Depot, a depot for the Department of Defense rotary wing aircraft.
The shooting comes months after a Saudi Air Force officer who was training at a Navy base in Pensacola, Florida, killed three US sailors and wounded eight other people in a shooting that American officials described as an act of terrorism.
The country's top federal law enforcement officials said this week that the gunman in December's attack, Mohammed Saeed Alshamrani, had been in touch with al-Qaeda operatives about planning and tactics in the months before the shooting. Alshamrani was killed by a sheriff's deputy.
According to US officials, unlike Pensacola, there are no international or foreign national students at the Texas base.