Police in Chandler, Ariz., confirmed to multiple Arizona media outlets that Keim was arrested on Wednesday morning during a traffic stop.
Keim, who could be in violation of the NFL policy on personal conduct, apologized in a statement released through the team.
"I truly regret my incredibly poor judgment and inexcusable actions," said Keim. "Everyone associated with the NFL and its teams is held to a high standard of behavior and I obviously failed to meet that. I sincerely apologize to our organization and its fans as well as to my family.
"I accept full responsibility for my actions and hold myself completely accountable. Moving forward, I will take the steps to ensure that I never put myself or the Cardinals in this type of situation again."
Keim has been with Arizona's organization since 1999, serving in a number of capacities. He was promoted to general manager in 2013.
"We are aware of the incident on Wednesday involving Steve Keim. He fully recognizes the seriousness of the situation and that this type of behavior is unacceptable and inexcusable," the Cardinals said in a statement. "Steve immediately alerted the team who in turn reported it to the NFL as required under the league's Personal Conduct Policy. We are continuing to gather information and will handle the matter appropriately and in accordance with all league policies as well as within the legal system."