A 4-month-old girl died this week after her father brutally assaulted her in their Lower East Side apartment — leaving her with a fractured skull, police said. 

Little Cairo Sanchez-Dixon died at NYU Hospital Monday morning, where her family had rushed her unconscious and unresponsive with head trauma, cops said. 

The medical examiner’s office found that Cairo suffered head trauma – including fractures to the rear and both sides of the skull, police sources said. 

The injuries were consistent with a blow to the head, as well as a fall, according to the sources. 

The infant’s father, Ceferino Sanchez, 34, had claimed to police that he was feeding his daughter the night before when he grabbed her to break a fall, police sources said. 

The investigation determined Sanchez was injured inside her home on Madison Street, within NYCHA’s Vladeck Houses, cops said. 

The infant’s death was found to be a homicide, and Sanchez arrested Tuesday and was charged with murder, manslaughter, reckless assault on a child and assault, cops said.  

The exact nature of the deadly assault was unclear Wednesday morning.