The fire broke out at about 12:50 a.m. at Colony Park Apartments on Peconic Street in Ronkonkoma.
When police arrived, they found the building fully engulfed.
At one point, police say the mother dropped her infant from a second-floor balcony into the arms of a bystander below, before jumping to the ground herself.
The woman and the infant were taken to Stony Brook University Hospital with minor injuries.
One man was also hospitalized with minor injuries.
Firefighters say residents in five units have been displaced. The cause of the fire is under investigation.
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