He had no symptoms on arrival but presented himself to a health facility on March 13, the ministry said. Rwanda is the 19th African nation to report the presence of coronavirus.
"He is currently under treatment in stable condition, isolated from other patients," the ministry said. "The tracing of all contacts has been conducted for further management."
RwandAir, Rwanda's national airline, announced it was suspending all flights to India until April 30 and would refund customers.
Africa had until now largely been spared the rapid spread of COVID-19, which has infected at least 127,000 people and killed 4,700 worldwide.
Other African nations to have reported cases of the virus include Morocco, Tunisia, Egypt, Algeria, Senegal, Togo, Cameroon, Burkina Faso, Democratic Republic of Congo, South Africa, Nigeria, Ivory Coast, Gabon, Ghana, Guinea, Sudan, Kenya and Ethiopia.