Fire officials say the 26-year-old was taken to Bellevue Hospital in Manhattan shortly after noon on Sunday. He was listed in critical but stable condition.
His aunt, Katharina Capatos, tells the New York Post it was lucky the city had the snow and hadn't cleared the garbage.
She says her nephew told her recently that he was worried about being evicted from his rent-stabilized apartment.
The city resumed garbage pickup on Monday for the first time since the Christmas weekend blizzard dumped over 20 inches of snow on the city.