The driver has been identified as 20-year-old Elijah Meredith.
Police were called to the 6900 block of Lancaster Pike in Newport around 10:30 a.m.
Investigators say the driver of a silver Mazda hit the child, identified as Leah Purdue, while leaving a home on the block, then fled the scene.
Meredith was located shortly before 12 p.m. and taken into custody without incident in Hockessin, police say.
After Leah was hit, her distraught mom scooped her up and ran to a neighbor's house.
"She had a pretty bad cut and blood was protruding down her face and over her body," said neighbor Ron Belile.
Jose Rivera was visiting inside the little girl's home on Friday when he heard the mother screaming at the driver of a silver Mazda, who was driving out of the driveway.
"She was trying to get the man to stop, to halt. He kept turning, trying to maneuver around her," he said.
Rivera then said the driver also hit Leah's mother.
"He hit the mom, and the baby, I am assuming, was under the car," he said.
VIDEO: Toddler struck in Delaware
The little girl's aunt, Linda Phipp, visited the child in the hospital.
"Right now she is asleep, she is doing good, no broken bones. She's got a fracture at the back of the skull, so they are watching that," she said.
The incident remains under investigation, police say.
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