FBI Director Kash Patel posted a photo on X of what he said was the suspect's unused ammunition that showed one with the words "ANTI-ICE" written along the side.
"While the investigation is ongoing, an initial review of the evidence shows an ideological motive behind this attack," Patel wrote.
In a statement, the Department of Homeland Security said the suspect fired "indiscriminately" at the ICE building, including at a van in the building's secured entry way where the victims were shot.
The department initially said two victims were dead and one injured, before later issuing a corrected statement that one detainee had been killed and two others were in critical condition.
Officials have not disclosed the identities of the victims.
The incident comes two weeks after the shooting death of conservative activist Charlie Kirk by a sniper during an event in Orem, Utah, which fuelled fears of a new wave of political violence in the United States.
The Associated Press, NBC News and Fox News, citing sources, identified the gunman as Joshua Jahn, 29.
A Reuters reporter interviewed Jahn's older brother, Noah, earlier in the day as Joshua Jahn's name began circulating online in connection with the shooting.
Noah, 30, said he was not aware that his brother harboured any negative feelings about ICE.
"I didn't know he had any political intent at all," said Noah Jahn, who lives in McKinney, Texas, about 50km north of Dallas, as did his brother.
At the time of the interview, Jahn said he was not sure whether his brother was involved but that he had begun to fear the worst after none of the family could reach him by phone on Wednesday.
A Reuters journalist saw FBI agents entering a house in McKinney at the address listed in online records for Joshua Jahn on Wednesday afternoon.
At a news briefing in Dallas, officials emphasised the investigation was still in its early stages.
Authorities were treating the attack as an "act of targeted violence," Joseph Rothrock, special agent in charge of the FBI's Dallas field office, told reporters.
Wednesday's shooter opened fire on the office from atop an adjacent building about 6.40am, police said.
Law enforcement officers were not injured in the shooting, officials said.
The attack took place at an ICE field office, not a detention facility, where ICE officers conduct short-term processing of recently-arrested detainees.
The aggressive use of ICE agents by US President Donald Trump's administration as part of its crackdown on undocumented immigrants has sparked outcries from Democrats and progressive activists.
Wednesday's attack was the third shooting this year in Texas at a Department of Homeland Security facility.
A police officer was shot in a July incident at an ICE detention centre in Prairieland and a 27-year-old Michigan man was shot dead by agents after opening fire on a US Border Patrol station in McAllen in July.
