Brown, a five-star cornerback prospect from Beaumont, Texas, was arrested Saturday night for failure to obey and resisting arrest.
During an appearance at the Senior Bowl on Tuesday, Saban said he has spoken to Brown since the incident. Saban also said that the team will "certainly try to use this as a learning experience for him."
"The punishment he receives will be so that he learns not to do something like this in a disrespectful way to somebody in a position of authority who is there to protect us all, which is our police," Saban said. "We're going to get him to learn from this."
Saban doesn't expect to have any more problems out of Brown going forward.
"Some people are in the wrong place at the wrong time," Saban said. "Some people don't make good decisions about what they do, what they say. Tony Brown's a fine young man and we're glad to have him in the program."
Brown, a two-sport athlete, was ranked as the No. 2 cornerback in the nation by 247Sports Composite ranking. He is also expected to participate for the Crimson Tide's track and field team.