The fire broke out at about 12:50 a.m. at Colony Park Apartments on Peconic Street in Ronkonkoma.
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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.
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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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