Some 961 people have died from the hemorrhagic fever in Sierra Leone, Liberia, Guinea and Nigeria since March during the largest Ebola outbreak in history.
"In responding to the request received this weekend from a West African nation, the available supply of ZMapp is exhausted," said a statement on the Mapp Bio website.
"Any decision to use ZMapp must be made by the patients' medical team," it said, adding that the drug was "provided at no cost in all cases."
The biomedical collaboration between US and Canadian researchers involves a drug that is manufactured in tobacco leaves and is hard to produce on a large scale.
The company did not reveal which nation received the doses, or how many were sent.
CNN reported that Liberia was to receive the sample doses.
The two American missionary workers who fell ill with Ebola while working in Monrovia last month were given doses of the drug.
Both have been transported to an isolation unit at Emory University Hospital in Atlanta, Georgia, where they are receiving continuous care.
A Spanish priest who was sickened with Ebola has also been given a dose.
The ethics of distributing experimental medications to some people but not others was the focus of a special meeting of the World Health Organization on Monday.
The US Centers for Disease Control and Prevention has repeatedly stressed that the drug's effects are unknown, since it has not been through a process of rigorous clinical trials.
There is no medicine or vaccine for Ebola on the world market.