The incident happened just after 11 p.m. in Suffolk County.
When firefighters arrived to the Mastic home, two were unconscious and four others were able to walk or be helped out.
Officials say a generator running in the basement of the home caused high levels of carbon monoxide.
Six people were removed from the home, with four transported to Long Island Community Hospital in East Patchogue for treatment.
The condition of the hospitalized family members was not disclosed.
None of the responding firefighters were injured.
The family had no power since Tuesday due to Tropical Storm Isaias.
Authorities say generators should always run outside of the home.
On Tuesday, a woman and her grandchild were sickened with carbon monoxide poisoning after exhaust from the generator they were using caused "fatal levels" of the gas inside a New Jersey home.
The home on Robin Road in South Brunswick was one of the one million buildings in the state affected by power outages caused by damage from Tropical Storm Isaias.
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