Tucson police said Tuesday that Fayde Riggin is being held on suspicion of first-degree murder and child abuse.
They say 2-month-old Mavrik Riggin died Monday after his father allegedly shook him multiple times over a month-long span.
The child's mother — 20-year-old Katherine Fitzgerald — also was charged Tuesday with child abuse.
Police say she allegedly knew her baby needed medical attention but failed to seek it.
Officers were called to the couple's home on Aug. 12 about an unresponsive baby.
Paramedics took the infant to a hospital with life-threatening internal injuries.
Police didn't immediately know Tuesday night if either Riggin or Fitzgerald had legal representation yet.