Melton, who is on injured reserve, was charged with assault and public intoxication.
"We are aware of the reports regarding Henry Melton," the Bears said in a statement. "We are currently gathering information to learn more about the circumstances surrounding the arrest."
Melton sustained a torn ACL in a Week 3 win over the Steelers.
The 6-3, 295-pounder was selected by the Bears in the fourth round of the 2009 draft out of Texas. He had a breakout year in his first season as a starter in 2011 when he recorded a career-high seven sacks, the third most by an NFL defensive tackle.
Melton was voted to his first Pro Bowl last season after registering 33 tackles with six sacks, five tackles-for-loss, a team-high 24 quarterback pressures and two forced fumbles.
After being sidelined for a month this summer after suffering a concussion in the preseason opener, Melton recorded three tackles in the Bears' first two games of the season. He stepped up his play in Pittsburgh, helping account for two of the defense's five takeaways before getting hurt.