The baby's mother was admitted to a hospital in Baton Rouge with symptoms of Covid-19 before going into labour three months early as her body fought the disease.
She remains in the hospital on ventilator support.
Dr Clark said the mother "went into pre-term labour and ultimately delivered the baby prematurely, and in doing so, the baby, because of the extreme prematurity, did not survive."
The coroner said the child has not tested positive for Covid-19 but doctors and the state's epidemiologist agreed that the death can be ruled a coronavirus-related death.
It's the first virus-related death of a newborn in the state.
Doctors are investigating whether coronavirus can be transmitted to a baby from the mother through vertical transmission.
The Centers for Disease Control and Prevention has found more the 2,500 confirmed cases of coronavirus in children between 12 February through 2 April. Roughly 6 per cent of those cases required hospitalisation. The agency confirmed three paediatric deaths.
The newborn was among seven virus-related deaths reported by Baton Rouge officials on Monday. Twenty-seven people in the state's capital have died following the outbreak.
Louisiana has identified nearly 15,000 confirmed infections in the state, including 512 deaths.
As of 6 April, 562 people are on ventilator support, though Governor John Bel Edwards said the hospitalisation rate is decreasing as officials point to the success of mitigation efforts and stringent social distancing measures that have been in place since early last month.
The pandemic has claimed the lives of more than 10,500 people in the US, according to data from Johns Hopkins University on Monday.
More than 356,000 people have been tested positive for the virus.
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