CNN correspondent Omar Jimenez and two colleagues were released within an hour after network chief executive Jeff Zucker called Walz to demand answers about why they were led away and held in a police van.
"We have got to ensure that there is a safe spot for journalism to tell this story," Walz said.
Jimenez and colleagues Bill Kirkos and Leonel Mendez were doing a live shot for CNN's "New Day" shortly after 5 a.m. Central Time, describing a night of fire and anger in the wake of Floyd's death after a Minneapolis police office knelt on his neck. Fired officer Derek Chauvin was charged with murder in that case later Friday.
When first approached by officers, Jimenez, who is black, told them, "put us back where you want us. We are getting out of your way."
After being told he was being arrested and his hands were tied behind his back, Jimenez asked why he was being arrested. He did not get an answer.
The Minnesota State Patrol said on Twitter that the journalists were among four people arrested as troopers were "clearing the streets and restoring order" following the protests. The patrol said the CNN journalists "were released once they were confirmed to be members of the media."
It's not clear why they were confused: Jimenez was holding what appeared to be a laminated ID card before his hands were secured, and his fellow crew members told police that they were from CNN and showing the scene live on the air.
"I've never seen anything like this," CNN "New Day" co-anchor John Berman said.
After being released, Jimenez said that he was glad that his arrest was shown on the air.
"You don't have to doubt my story," he said. "It's not filtered in any way. You saw it for your own eyes. That gave me a little bit of comfort. But it was definitely nerve-wracking."
At a later news conference, Walz said that "I take full responsibility. There is absolutely no reason something like that should happen ... This is a very public apology to that team."
The arrest drew widespread condemnation across the news industry. CNN competitors MSNBC, CBS News and Fox News all issued statements in support of Jimenez, along with the Society of Professional Journalists and the National Association of Black Journalists.
CNN accepted Walz's apology, saying the network appreciated the sincerity of his words.
Walz's words in support of journalists have impact at a time when the news media is often under attack, said Jane E. Kirtley, Silha Professor of Media Ethics and Law and director of the Silha Center at the University of Minnesota.
"It's really important for the governor to make that kind of statement to emphasize to everyone, especially law enforcement, that the press has an important job to do ... and they need to be respected," said Kirtley, who lives blocks away from the protests and could still smell smoke from the fires on Friday.