Walz, a Democrat, said in a social media post that he had been in contact with the White House after the shooting.
He called on Trump to end the crackdown in his state.
The details surrounding the shooting were not immediately clear.
Minneapolis officials said they were looking into reports that a man had been shot in south Minneapolis.
"We ask the public to remain calm and avoid the immediate area," a post by the City of Minneapolis read.
DHS spokeswoman Tricia McLaughlin told the Associated Press in a text messages that a person who had been shot had a firearm with two magazines and that the situation was "evolving".
DHS also distributed a photo of a handgun they said was on the person who was shot.
A 51-year-old man shot on Saturday by federal immigration officers in Minneapolis had died, a hospital record obtained by the Associated Press showed.
After the shooting, an angry crowd gathered and screamed profanities at federal officers, calling them "cowards" and telling them to go home.
One officer responded mockingly as he walked away, telling them: "Boo hoo".
Agents elsewhere shoved a yelling protester into a car.
The shooting happened a day after thousands of demonstrators protesting the crackdown on immigrants crowded the city's streets in frigid weather, calling for federal law enforcement to leave.
Protesters have gathered daily in the Twin Cities since January 7, when 37-year-old mother of three Renee Good was fatally shot by an Immigration and Customs Enforcement officer.
Federal law enforcement officers have repeatedly squared off with community members and activists who track their movements.
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