The boy tested positive last week and died late on Monday at a treatment centre near the capital, Monrovia, Francis Kateh, the chief medical officer, said.
The deceased boy's mother and two other siblings have also been admitted to the treatment centre to be monitored.
About 160 people are being monitored since the new cases of Ebola was confirmed. This includes eight healthcare workers "who are at high risk because they came in direct contact with the boy."
The World Health Organization (WHO) has twice declared Liberia to be Ebola-free, once in May and again in September.
With the new cases, radio and television stations have resumed broadcasting Ebola awareness messages.
Civil society groups have also stepped up a campaign to get volunteers to be vaccinated against the disease in a joint US-Liberia Ebola trial, according to a BBC reporter.