Josh Blank suffered burns over more than 70 percent of his body after a woman, Rhonda Kavee, doused the grill with alcohol in an attempt get a fire started, The New York Daily News reported Monday.
The boy was reported in critical but stable condition at New York-Presbyterian Hospital Weill Cornell.
Kavee was having a birthday party for son at her Manhattan dental office and was trying to light a grill so the children could toast marshmallows, investigators said.
Police said heavy rains had forced the planned cookout indoors.
A source told the newspaper police considered the incident an accident but were working with the Manhattan district attorney's office to determine if any charges are warranted.