White House spokesperson Abigail Jackson confirmed the US president's authorisation, citing what she called "ongoing violent riots and lawlessness" that Chicago leaders have not quelled.
"President Trump will not turn a blind eye to the lawlessness plaguing American cities," Jackson said.
Governor JB Pritzker called the move unnecessary and "a manufactured performance - not a serious effort to protect public safety."
"This morning, the Trump Administration's Department of War gave me an ultimatum: call up your troops, or we will," Pritzker said in a statement.
"It is absolutely outrageous and un-American to demand a governor send military troops within our own borders and against our will."
Meanwhile the Department of Homeland Security acknowledged the shooting of the woman in Chicago.
It said in a statement that Border Patrol agents on patrol "were rammed by vehicles and boxed in by 10 cars," and when they got out of their trapped vehicle, "a suspect tried to run them over, forcing the officers to fire defensively."
The woman was a US citizen and was armed with a semi-automatic weapon, DHS spokesperson Tricia McLaughlin said, noting she was accused in a US Customs and Border Protection intelligence bulletin last week of doxing agents.
The woman was treated and later released, according to Mount Sinai Hospital.
The escalation of federal law enforcement in Illinois follows similar deployments in other parts of the US. Trump deployed the National Guard to Los Angeles and as part of his law enforcement takeover in Washington. Meanwhile Tennessee National Guard troops are expected to help Memphis police.
California Governor Gavin Newsom sued to stop the deployment in Los Angeles and won a temporary block in federal court. The Trump administration has appealed that ruling.
Federal officials reported the arrests of 13 people protesting on Friday near the facility, which has been frequently targeted during the administration's surge of immigration enforcement this fall.
Trump also said last month that he was sending federal troops to Portland, Oregon, calling the city war-ravaged. But local officials have suggested that many of his claims and social media posts appear to rely on images from 2020, when demonstrations and unrest gripped the city following the killing of George Floyd by Minneapolis police.
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