Jorge Colon, 20, of Oxford, Pa., is charged with aggravated assault, endangering the welfare of children and related charges.
The child has previously been diagnosed with colic after her parents sought medical attention because of her continued crying.
Police say Colon has two children with the baby's mother, who was taking a shower during the incident Saturday.
Colon was giving the baby a bath in the sink, investigators say, when the child started crying.
Colon became frustrated, lost his temper and, according to police, turned the water up to a scalding hot temperature as the baby screamed.
He then wrapped the baby in a towel but, when he removed the towel, saw the baby's skin was peeling from the burns.
Colon and the baby's mother took the child to Jennersville Regional Hospital. The baby was then transferred to the Burn Unit at Crozer-Chester Medical Center where she remains in critical condition.
The baby suffered first and second degree burns over 40% of her body, the D.A. said.
In a written statement, Oxford Police Chief John Slauch said, "I have been a police officer for 38 years. This is one of the worst cases of child abuse I have ever seen in Chester County."
District Attorney Tom Hogan said, "As a prosecutor, I am outraged that anybody would harm a baby. As a father, I am deeply saddened and disturbed that a father could do this to his own daughter."
Colon is being held on $125,000 bail.