Philadelphia police said Wednesday that a person of interest is in custody and the vehicle involved has been recovered.
No further details about that person have been released.
Police said the two victims were struck at Broad and Arch streets just after 10 p.m. when a dark grey Jeep was being followed by police.
Police originally thought the woman's three children were all hit by the Jeep, but only one of the children was hit and injured.
The 38-year-old woman was taken to Jefferson Hospital with "severe head trauma," but Philadelphia police said she passed away at 1:23 p.m. Wednesday.
The 8-year-old child, who suffered internal injuries and head trauma, was taken to CHOP where she was placed in the ICU.
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The two other children, who are 10 and 11 years old, were not injured and are in the care of social workers, police said.
Police said a witness told them the children were calling for their mother after the crash as medics worked on her.
The incident started when an officer saw the Jeep speeding the wrong way on the 1400 block of JFK Boulevard in Center City.
Police said the officer followed the vehicle and then more officers spotted it speeding on Arch Street in the right direction at 8th Street with its headlights off.
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Those officers followed the Jeep along Arch past Reading Terminal Market and the Pennsylvania Convention Center to the area between 13th and Broad Streets in front of Trader Joe's.
That's where police said the Jeep struck the mother and child, launching the woman at least 20 feet.
The driver of the Jeep kept going, but the officers had to stop to help the victims, police said.
The investigation into the crash is ongoing.