The live video showed Minnesota State Patrol handcuff CNN reporter Omar Jimenez and lead him away. A producer and a photojournalist for CNN were also taken away in handcuffs.
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."
"We told you before that we are with CNN," the cameraman is heard telling police.
The cable news network said Jimenez, a black man, was arrested while a white reporter on the ground was not. In a tweet, CNN Communications said that the crew identified themselves and called the situation a "clear violation of their First Amendment rights."
Jimenez and his crew have since been released, CNN confirmed. He went back on air soon after and called the situation "confusing."
CNN president Jeff Zucker spoke to Minnesota Gov. Tim Walz, who apologized for the arrest. Walz said he takes full responsibility for what happened.
"We want the media there to cover this. It is never acceptable for this to happen. The governor accepts full responsibility," Walz said.
The Minnesota State Patrol said on Twitter that the journalists were among four people arrested as troopers were "clearing the streets and restoring order." The patrol said they "were released once they were confirmed to be members of the media."
Minneapolis and nearby St. Paul have seen days of violent protests over the death of George Floyd, a handcuffed black man who pleaded for air as a white police officer kneeled on his neck.
The Associated Press contributed to this report.