More than 50 doctors, nurses and technicians were involved in the operation at Dhaka's Bangabandhu Medical College Hospital to separate conjoined twins Banya ("Flood") and Barsha ("Rain").
Paediatric surgeon Shafiqul Haq said Barsha, who had been on artificial respiration following the surgery, died on Wednesday evening.
"In these cases one of the twins is always stronger than the other and in this case Barsha was not the strong one and has died," Haq told AFP, adding that doctors were hopeful Banya would survive.
"The condition of the other twin is good. She has a little bit of fever. It is too early to determine whether the surviving twin is risk-free."
The children, born in northern Bangladesh, were joined at the stomach and chest with separate heads and limbs.
Their mother, a nurse, brought them to Dhaka, where they were monitored for three weeks before doctors decided to go ahead with the seven-hour operation.
Three previous operations in Bangladesh to separate conjoined twins in the past four years have resulted in the deaths of all but one child.