Abraham Borbor was one of three doctors in Liberia who had been given ZMapp and were showing signs of recovery.
ZMapp has been credited with helping several patients recover, including two US doctors.
More than 1,400 people have died from Ebola this year in four West African countries – Guinea, Liberia, Nigeria and Sierra Leone.
Dr. Abraham Borbor “was showing signs of improvement but yesterday (Sunday) he took a turn for the worse,” Liberian Information Minister Lewis Brown told the BBC.
“What this means for the drugs, I don’t know,” the minister added, without giving further details.
It is believed Dr. Abraham Borbor died in the capital Monrovia. He was the deputy chief medical doctor at the country’s largest hospital.
Liberia has recently imposed a quarantine in parts of Monrovia to try to stop the spread of the virus.
Last Thursday, police fired live rounds and tear gas during protests among residents of the city’s West Point slum.
Liberia has seen the most deaths – more than 570 – in what is now the worst Ebola outbreak in history.
Meanwhile, Japan said it was ready to allow shipments of an experimental anti-viral drug to help combat the Ebola outbreak.
It is not clear whether T-705 (or Avigan) will actually work against Ebola, and no monkey or human trials of the drug have been done.
T-705 was developed by Japan’s Toyama Chemicals company for use against new strains of influenza. It was approved by the Japanese government earlier this year.
A company spokesman says the firm believes the similarity between flu viruses and Ebola means Avigan could be effective.
Japan says it is ready to ship Avigan even without approval by the World Health Organization (WHO).
Ebola is spread between humans through direct contact with infected body fluids and several doctors and health workers have died.
It is one of the world’s deadliest diseases, with up to 90% of cases resulting in death, although in the current outbreak the rate is about 55%.
The speed and extent of the outbreak was “unprecedented”, the WHO said last week.
An estimated 2,615 people in West Africa have been infected with Ebola since March.
On Saturday, Sierra Leone’s parliament passed a new law making it a criminal offence to hide Ebola patients.
If the law is approved by the president, those caught face up to two years in prison.
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