Flames broke out in apartment 3A at 60 Moore Street shortly after 1 a.m., according to firefighters.
Video of the rescue showed a ladder raised to an apartment window as a firefighter carried the baby girl that was passed to him through a window. The baby was not injured.
Several other people were also rescued.
Eleven people were injured including two firefighters. Six people including the baby were taken to a local hospital. They were expected to recover.
The cause of the two-alarm fire was not clear.
A resident told reporters a space heater in her apartment caught fire.
"When I got up I went to the kitchen and I just couldn't believe that my space heater was on fire. It was on a low flame. I called 911. As soon as the fire went up more, I tried to get water, I just ran out. I grabbed my child and ran out."
The woman said she left without shoes, a jacket or money.