Emergency personnel using robotic devices after firefighters were pulled back from the fallen structure due to unstable conditions checked the site for any further casualties, but officials said they believed all victims had been accounted for.
No foul play was suspected.
"We have no reason to believe that this was anything other than a structural collapse," City Police Commissioner Keechant Sewell told reporters on Tuesday.
Reuters video footage from the scene, in Manhattan's financial district blocks from the World Trade Center and New York Stock Exchange, showed a rescue operation under way and multiple cars stacked on top of one another amid crumpled slabs of concrete.
One person was pronounced dead at the scene, four more were taken to area hospitals for injuries and a sixth individual who was hurt declined medical treatment, chief of fire operations for the New York City Fire Department John Esposito said.
He described all six as workers who were in the parking structure when it collapsed.
"This was an extremely dangerous situation for our firefighters," he told reporters.
Esposito said firefighters ordered out of the structure had still been inside conducting searches as "the building was continuing to collapse".
Robot devices were then deployed, he said, marking the first time city firefighters had flown a drone aircraft into a fallen building to conduct a search.
Pace University, a private college campus whose students, faculty and staff use the parking structure, was evacuated as a precaution, authorities said.
"This building is completely unstable," New York City Mayor Eric Adams told reporters.
The New York City Department of Buildings' online records showed the structure at the site of the collapse had been cited for 45 violations, including 25 since 2003, many related to its elevators.
One 2003 filing noted "ceiling slab cracks exist" as well as "defective concrete with exposed rear cracks".
It said an $US800 ($A1189) fine had been paid for the violation.
Eyewitnesses said the collapse was swift and without warning.
"It all happened so fast," said Thai Nguyen, 35, who lives in Chinatown and is a manager of the nearby Kollective Klub.
"Our store is two buildings from the parking garage, and we also have a hotel next to us. People ran inside asking if they could take refuge inside our store."
Sandy Imhoff, 78, who lives in an adjacent apartment on the same street, said she fled her home with her two cats when her building began to shudder from the force of the collapse.
"My building was shaking. I only had time to grab my dog and leave," she said.
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