The blaze broke out just before 5:00 a.m., in the unit block of Elmer Street in Bridgeton.
When firefighters arrived they found flames and heavy smoke, and were told that several people were trapped inside.
Firefighters had to get to the trapped victims by climbing ladders to second and third floor windows.
When one firefighter reached the third floor he found a girl holding a baby girl.
Bridgeton Fire Chief David Schoch said the girl handed the infant to the firefighter, but when the firefighter started descending the ladder, the girl at the window panicked and jumped toward the ladder.
Schoch said, the girl then, "landed on top of him (the firefighter). And actually landed on top of his shoulder and his head, and he's trying to hold onto the ladder, the baby and her."
Schoch said when the three of them were about eight feet from the ground, the girl fell.
She and the infant have been taken to the hospital, where there's no word on their exact condition.
The baby had suffered burns.
The three other people who were rescued are not injured.
The Red Cross is finding shelter for those who are now homeless because of the fire.
Investigators are looking for a cause.
