Minneapolis officials asked for calm and said the man was hospitalized with apparently non-life-threatening injuries.
Tensions in the city have been running high since Good's death and the federal government's increased immigration enforcement.
DHS said officers were attempting a traffic stop of a Venezuelan man, who they said is in the country illegally.
As the officer pursued the man, he assaulted the officer, according to the statement.
The original man then got loose and also began attacking the officer with a shovel or a broomstick, the department said.
Minneapolis Police Chief Brian O’Hara said the officer shot the man during a struggle outside a home north of downtown Minneapolis.
Federal officials say the officer shot Good in self-defense, while others have sharply rejected DHS’ narrative. »