Anti-ICE protesters quickly gathered at the scene on Sunday.
The unnamed man was in serious but stable condition at a hospital after being shot once in the torso on the city's north side, Austin Police Chief Lisa Davis said at a news conference with the mayor and other city officials.
The Department of Homeland Security, which oversees ICE, did not participate in the news conference and didn't immediately respond to requests for details.
Austin police officers were not involved in the operation or the shooting, which occurred after a traffic stop, Davis told reporters.
Austin Mayor Kirk Watson, a Democrat, said he wants the city's police department to be involved in the investigation so it can provide "clear, third-party eyes" in the process.
Watson said he does not think it would be appropriate for ICE to conduct an investigation on its own.
Austin residents have "a right to feel safe in their city," Watson said.
A proper investigation will only enhance credibility, he added.
Davis said she did not yet know the nationality of the person who was shot.
The shooting comes as ICE surges enforcement across the country this northern summer, producing more than 50,000 arrests a month for the first time in its history in July and August.
In July, an ICE officer fatally shot 52-year-old Lorenzo Salgado Araujo, of Houston, after federal agents driving unmarked vehicles pursued him while he was taking his construction crew to a job site.
Also in July, 25-year-old Johan Sebastián, a Colombian man, was shot by an ICE officer in Maine.
The administration's enforcement efforts were widely condemned last winter after the killings of Alex Pretti and Renee Good in Minnesota.
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