The baby was admitted after a visit to the emergency department of the hospital in Solna in December 2008 with symptoms including a high fever, writes newspaper Svenska Dagbladet.
After being diagnosed with pneumonia, the parents noticed her condition began to deteriorate the following day and made a number of attempts to bring their concerns to the attention of medical staff.
They say the hospital only took action when her heart stopped beating.
“It still feels unreal that we could be so ill-treated and ignored,” they said. “She died in front of our eyes without anyone caring before it was too late.”
The baby was left brain dead and a decision was taken three days later to switch off a life-support machine.
The case has now been handed over to Sweden’s Medical Responsibility Board (HSAN) for investigation.
The hospital admits that the baby’s symptoms were not followed up according to correct procedure.
Senior doctor Svante Baehrendtz said there are obvious shortfalls in the quality of care she received.
“We have taken actions to ensure this never happens again,” he told SvD.
The hospital faces mounting pressure after a number of negligence cases have been reported.
Last year, a baby was mistakenly prescribed a dose of painkillers ten-times higher than the recommended level.
In 2008, a newborn died after a similar incident but both staff and the hospital was vindicated in both cases after investigation.