Police were called to the scene of the crash in the intersection of West 4th and N. Lincoln streets just after 10:00 p.m. Wednesday.
Police say two cars, a Mitsubishi Galant and a Hyundai, collided in the intersection.
Inside the Mitsubishi were a 25-year-old woman and her two children, a 4-year-old girl and a 6-year-old boy.
Police say the girl was pronounced dead at the scene while the boy died later at the hospital.
The driver of the Hyundai, a 40-year-old woman, fled the scene on foot but, police say, she was apprehended a few blocks away.
Police say she was the only person in that car.
Investigators say they learned the woman, who has not yet been identified, was already wanted by police on undisclosed charges and - for now - is being held on those charges.
The names of those involved have not yet been released.
Anyone with information regarding this incident is asked to contact the Wilmington Police Department Traffic Division at 302-576-3692.