The man, who was shot in the torso, was taken to a local hospital in serious but stable condition, officials said at a news conference.
Austin Police Chief Lisa Davis said the shooting occurred shortly before 1 p.m. (1800 GMT) and that she had not yet been fully briefed by federal officials.
Immigration attorney Kate Lincoln-Goldfinch identified the man as Wilber Rafael Garces Perez, 28, and said she represents his family.
Lincoln-Goldfinch said Perez was released from the hospital on Sunday into the apparent custody of ICE.
A law enforcement source told CNN that Perez is an undocumented immigrant from Venezuela, while Lincoln-Goldfinch told the Texas Tribune that her client entered the United States legally.
ICE and the US Department of Homeland Security did not immediately respond to requests for comment.
City officials did not identify the man who was shot or the ICE agent involved, saying they did not know the agent’s identity and that local authorities had received limited information from federal officials.
The incident has intensified scrutiny of ICE, which has become a central component of the Trump administration’s immigration crackdown and has faced calls from rights advocates and local officials for greater accountability.
Calls for police investigation
Austin Mayor Kirk Watson, a Democrat, said he wants Austin police involved in the investigation, with additional participation from the Texas Rangers.
“From my perspective, the credibility of ICE doing some form of an investigation just by itself and excluding others would not be appropriate,” Watson said, adding that he is angry about the shooting but not surprised by it.
Watson and US Representative Greg Casar, a Texas Democrat, said ICE has recently increased detentions in Austin.
“Just a few weeks ago, as we saw the ICE surge come to Austin, especially to North Central Austin, I and others said that ICE needed to leave before someone was shot,” said Casar, whose district includes parts of Austin.
Meanwhile, local television coverage showed protesters gathered across the street from a blue Toyota Corolla that had sustained damage to its passenger-side door, while ICE agents stood nearby.
Rights advocates have accused the federal immigration crackdown under US President Donald Trump of violating free speech and due process rights, while Trump has defended the policy as an effort to improve domestic security.
The Austin shooting comes amid broader scrutiny of federal immigration officials following multiple shootings this year, including the killings of two US citizens in Minnesota, which triggered widespread backlash.
More than 50 people have died in ICE detention since Trump returned to office last year.
Casar cited the killing of US citizen Renee Good in Minnesota earlier this year as evidence that, in his view, ICE cannot be relied upon to provide accurate information about shootings involving its personnel.
“It is important for us to have transparency and the true facts in this case,” he said.
“Unfortunately, ICE has not been truthful in shootings in other cities.”