The soldiers are part of the 11th Airborne Division in Fort Wainwright, the official added.
In a Sunday interview on CBS Face the Nation, Minneapolis Mayor Jacob Frey condemned Trump's threat to send more troops into the city, saying the existing presence of federal ICE agents is already an "occupying force that has quite literally invaded our city".
"You can go through whatever rhetorical flourish you want, but when you have 3,000 ICE agents and border control come to the city, when you've got this supposed threat of 1,500 military coming to the city, yeah, that's very much what it feels like," Frey said.
Last week, Trump threatened to invoke the Insurrection Act, a rarely used law that allows active-duty military personnel to be deployed for law enforcement duties inside the US.
It comes as a US federal judge issued an order limiting the crowd control tactics that can be used by ICE agents towards "peaceful and unobstructive" protesters in Minneapolis.
On Friday, Judge Katherine Menendez ruled that federal agents cannot arrest or pepper spray peaceful demonstrations, including those monitoring or observing ICE agents.
But Homeland Security Secretary Kristi Noem said in a Sunday interview on CBS's Face the Nation that the judge's ruling is "a little ridiculous" because it "didn't change anything".
"We only use those chemical agents when there's violence happening and perpetuating and you need to be able to establish law and order to keep people safe," Noem said. "So that judge's order didn't change anything for how we're operating on the ground, because it's basically telling us to do what we've already been doing."
The state's National Guard has been mobilised and placed on alert by Governor Tim Walz, and other law enforcement officers were deployed to Minneapolis ahead of the anti-ICE demonstrations.
Recent protests in the city were sparked by widespread action by ICE in the city, and follow Good's death on 7 January.
City leaders said Good was there as a legal observer of ICE activity.
But the Trump administration has called her a "domestic terrorist".
Good's death sparked protests across the country, with many people holding signs that read "Justice for Renee".