Fahim Shikder, 14, died at the burns unit of Dhaka Medical College Hospital around 11pm Saturday.
"He had 95 percent burn injuries." resident physician Partha Shankar Pal told bdnews24.com.
The seventh-grader was burnt along with his grandmother Parul Akhtar when the air conditioner in their flat at Old Dhaka's Tipu Sultan Road exploded on Saturday night.
The 65-year-old received 37 percent burns and was still at the hospital.
Fahim and Parul were rushed to Dhaka Medical College Hospital, Wari Police Station OC Md Jihad Hossain had told bdnews24.com.
He said Fahim's father Foysal Shikder, mother and brother were mildly injured in the explosion.
Foysal, an aluminium trader, lived with his family on the second floor of the four-storey building.