White allegedly struck UNC senior Paul Britt in the face after what was described as a "verbal altercation" early Sunday in a parking lot at the corner of Rosemary and Columbia streets.
Davis is in the process of taking disciplinary action. This is the first arrest of a football player since he took the coaching post in November and his second disciplinary action.
Earlier this month he dismissed offensive lineman Charlston Gray from the team for repeatedly violating team rules.
Davis released a statement after the incident became public.
"I expect our student-athletes to represent North Carolina in a first-class manner both on and off the field, and I will not tolerate this type of behavior," he said in his statement. "We will discipline Garrett and also monitor the judicial process related to his case."
According to Chapel Hill police reports, White left the scene in a vehicle with two others before he was found and arrested based on the victim's description.
White declined to comment Thursday through a Department of Athletics spokesman.
Britt stated in an e-mail that the incident was instigated by an exchange of remarks about a woman who was with Britt.
White is scheduled to appear in court April 10. Britt stated in the e-mail that he does not want to appear in court or press charges.
"I hate that it was one of our football players and hope his coach doesn't take it out on him too bad," the e-mail states.
The code of conduct for student-athletes states that those charged with misdemeanors can continue participation on a team but that the decision must be made by Director of Athletics Dick Baddour and the coach.
"Every situation obviously is taken into account in its own separate way," said Larry Gallo, senior associate director in the Department of Athletics. "Certainly we also want to be fair in every sense of the word and let the accusations play out."
While he was football coach at the University of Miami, Davis suspended three players who were involved in the assault of a track athlete.
Before Davis's appointment to the Miami position, the team had one of the largest numbers of assault charges of any college football team nationally.
Former UNC coach John Bunting was known for taking disciplinary action quickly. He dismissed three players from the team in 2004 when they were caught with marijuana.
The athletics department is notified whenever a student-athlete runs afoul of the law. The department receives a daily briefing from the Chapel Hill Police Department.
"It's a situation that the coach would be aware of first off and would take the necessary discipline action," said Kevin Best, director of football communications.