The fire began in a third floor apartment at 500 East Houston St., near the FDR, about 4:16 a.m., an FDNY official said.
"I was sleeping. My neighbor came knocking on my door. He said, 'Fire! Fire!' He said he fell asleep with his cigarette in his hand and it fell to the floor," said third-floor tenant Carmen Santiago, 53.
"The smell was really strong. It was scary. ...I grabbed my Jack Russell and we took the stairs down."
A civilian suffered minor injuries but refused medical attention at the scene, the official said.
A firefighter was treated for a minor injury at New York-Presbyterian/Lower Manhattan Hospital, an FDNY spokeswoman said.
The firefighters brought the blaze under control about 4:50 a.m., officials said.
"They got here fast. They did a good job," Santiago said.