Dera Nur Anggraini was born prematurely with her twin sister Dara on February 10, with a throat deformity that obstructed her breathing, said father Elias Setya Nugroho.
He said his family searched for treatment but was turned away from 10 hospitals, with some claiming not to have the right equipment and others saying they were fully occupied.
"Dera was buried yesterday, on Sunday, not far from our home," Nugroho said, adding the baby died after being taken back to the Zahira Hospital in Jakarta where she was born.
"We tried several hospitals but they were full. Finally we went to a private hospital but we couldn't pay. In total 10 hospitals rejected us," the street sandal vendor told AFP.
He said the private hospital asked for a down payment of 15 million rupiah ($1,552), even though the family held a health card that entitles low-income earners to free health services.
He said his other daughter Dara, who was born weighing 1.4 kilograms (three pounds) was now in a public hospital fighting for her life.
Health Minister Nafsiah Mboi said the baby who died would have had little chance of survival.
"The baby was born weighing just one kilogram, so she had little chance of survival. Usually babies are around three kilograms when they're born," she said.
But the minister admitted the city was under-resourced to handle complications with newborns.
"The family was looking for a place for their baby. There are only 10 neonatal intensive care units (in Jakarta) and they were all full," Mboi told reporters.