The accident happened just after 8:00 a.m. at the intersection of Lancaster Avenue and Rodman Street.
Police say one of the children was thrown from a stroller on impact.
The victims, an 18-month-old girl, a 10-month-old boy and the 21-year-old woman, were taken to Christiana Hospital in stable condition - all having suffered non-life threatening injuries.
The woman was treated for internal injuries. The children suffered multiple abrasions.
The driver of the striking SUV did stop and remained on scene.
There are no traffic lights, stop signs or crosswalks at the intersection where the accident took place.
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