Ryan Louis Mosqueda fired dozens of rounds at the entrance of the facility shortly before 6am and agents returned fire, McAllen police chief Victor Rodriguez told reporters.
A McAllen police officer was shot in the knee during the exchange of fire and was taken to hospital, Rodriguez said.
The US department of homeland security said a border patrol employee was also injured.
Law enforcement found additional assault firearms and more ammunition in Mosqueda’s Chevrolet passenger car, which was parked nearby, Rodriguez added.
“There were many, many, dozens of rounds fired by the suspect towards the building and agents in the building,” he said.
Writing, thought to be Latin, was spray-painted on the side of the vehicle, but Rodriguez did not provide details of what it said or whether it gave any indication of the motive for the attack.
Pictures published on social media showed “Cordis DIE,” a Latin phrase meaning “Heart Day”, written in black spray paint on the driver’s door of the white, two-door car. The name also refers to a fictional populist revolutionary movement in the “Call of Duty: Black Ops II” video game, according to fan websites.
The facility where the shooting took place houses border patrol’s special operations teams, according to a former US customs and border protection official.
Mosqueda is believed to have ties to the area, as he was reported missing at 4am from a residence in Weslaco, about 18 miles (29km) east of McAllen, Rodriguez said, without giving further details.
The FBI is leading the investigation as it involved an attack on federal officers and a federal building, Rodriguez said.
Flights at the nearby McAllen International Airport were delayed for several hours as law enforcement secured the area.
A member of border patrol’s tactical unit, known as BORTAC, helped stop the alleged shooter, the former CBP official said, requesting anonymity to share details of the incident.
President Donald Trump, a Republican, has made combating illegal immigration a top priority, sending troops to secure the US-Mexico border and launching aggressive raids in US cities.
The actions – supported by Trump’s hardline Republican base – have also led to pushback from Americans concerned about arrests of non-criminals and enforcement tactics that include officers wearing masks to hide their identities.
The number of migrants caught crossing the border illegally has fallen to record lows under Trump, including a new monthly low of about 6,100 in June.
In 2020, during his first term, Trump deployed BORTAC agents to the city of Portland, Oregon to protect federal buildings after attacks on a federal courthouse during protests against racism and police brutality.