Tucson police said Wednesday night that 18-year-old Anthony Esparza is being held in the Pima County Jail.
They say the baby remains hospitalized in critical condition.
Police were called to Kino Hospital early Tuesday about an infant brought in by her parents with life-threatening head trauma.
The girl was transferred to University of Arizona Medical Center due to the serious nature of the injuries.
Police say investigators determined that the child was intentionally dropped.
They say the baby allegedly was in the care of Esparza at the time of the incident.
It's unclear if Esparza has legal representation yet.