Jillian Ludwig, 18, was walking on the track in the Edgehill Community Memorial Gardens Park when she was hit by a stray bullet.
She is said to be in extremely critical condition at Vanderbilt Medical Center.
Police said the gunfire came from public housing across the street and a suspect is in custody.
Shaquille Taylor, 29, is being charged with aggravated assault and evidence tampering in connection to the shooting.
Police said he was shooting at a car when the bullet hit Ludwig in the head.
The president of Belmont University, Dr. Greg Jones, sent a letter to students and faculty that said Ludwig is known for her love of music.
She is a music business major and bass player who loves running and enjoys being outside.
He said a prayer service would be held on campus Wednesday afternoon and asked the community to join him in praying for Ludwig's family, friends and loved ones.