The two-year-old girl was thought to be in a life-threatening condition, despite showing no physical injuries at the scene.
She was hit at the junction of Susans Road and Tideswell Road at around 5.20pm but police and ambulance services did not at
tend.
The youngster was later taken to Eastbourne DGH by taxi with her parents when she became unresponsive and was rushed to Guy's in an ambulance.
Concerned medics at Eastbourne contacted police and the female driver of a white Renault van was arrested on suspicion of drink driving, failing to stop at the scene and failing to report an accident.
The driver, believed to be an Eastbourne woman, was remanded in custody but later released on police bail without being charged.
Police arrived at Susans Road at around 6.45pm and closed the area for around half an hour while they carried out investigations at the scene.
Sergeant Steve Dessouki-Harman, at Polegate Road Traffic Police, said, "The vehicle skidded but we believe it was a low-speed impact and the van was travelling at less than 10mph.
"We were unaware of the incident until staff at Eastbourne DGH alerted us.
"The staff thought it was serious enough to send the child to Guy's as she became unresponsive but by 4am on Saturday she was up and chatting to her dad."
The two-year-old was sedated, ventilated and given a CT scan but no injuries were found by medics at Guy's and she left the hospital the next day.
Sussex Police are appealing for witnesses and ask anyone who saw the crash to call 0845 60 70 999 or Crimestoppers on 0800 555 111, quoting Operation Kingsbury.
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