Bidwill told radio station KFYI on Tuesday that Keim made an "enormous mistake," referring to the general manager's arrest on charges of driving under the influence in Chandler, Ariz., on Wednesday.
"First of all, I'm extremely disappointed," said Bidwill. "It's inexcusable. He did bring it to our attention right away that night and has been extremely remorseful and contrite. He's taken steps to make things right, but the reality is that there is a process in place that the league has and there are going to be consequences here."
Keim, who apologized in a statement released through the team following his arrest, could be subject to disciplinary action for a violation of the NFL policy on personal conduct.
More details from the incident became available Tuesday with the release of the police report, which noted that Keim refused to participate in a number of sobriety tests. Keim willingly provided his name to officers, according to the report, but he identified himself as the team's director of security.
Police noticed Keim was driving "erratically" and smelled alcohol on his breath. He told police that he had two beers while eating pizza.
"I truly regret my incredibly poor judgment and inexcusable actions," said Keim in the statement. "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.