Webb, 24, was pulled over for speeding on Interstate 57. He was originally charged with possession of a controlled substance -- cannabis -- and drug paraphernalia.
Webb was released Monday on a $500 bond.
The Bears said in a statement Wednesday that the team is aware of Webb's arrest and is "currently gathering information to learn more about the circumstances surrounding the arrest."
Webb apologized on Twitter Wednesday afteroon, tweeting, "Headed to Texas to train. I apologize."
