The four-to-five week old kitten was found on Thursday afternoon on F Street near McPherson Square Park.
A Good Samaritan, Damaris Alcala, found the kitten, which is being cared for by veterinarians.
"It was crying when I was picking him up, but when I moved him in the back, he was screaming," Damaris said.
The SPCA says the baby cat has burns over a third of its body, with most of the burns on its head and back.
The kitten is being treated at Crown Veterinary Hospital in Lebanon, N.J., and is expected to make a full recovery, the Humane Society said.
The $5,000 reward is for information leading to the identification, arrest and conviction of the person or persons responsible.
Anyone with information about the case is asked to call (866) 601-SPCA.