The blaze broke out on the morning of April 22 at Ljubica Ivezic orphanage, downtown in the Bosnian capital, and quickly spread to three rooms where the babies were sleeping, fire officials said.
Three baby boys and two girls were killed.
The latest victim - a seven-month-old baby boy who died Friday - had been among 17 children injured in the fire. A nurse also suffered burns on her hands and face while trying to save the children from the flames.
"The little boy died on Friday. His tiny body just could not survive the extensive burns he suffered," said Biljana Jandric, spokeswoman for Sarajevo Kosevo's hospital.
The fire left the orphanage scattered with charred cradles, baby beds and teddy bears.
Firefighters rescued 23 children from the three rooms, and extinguished the flames within about 15 minutes.
Authorities are still investigating the cause of the fire.