Public Health England (PHE) said the patient was a resident of Nigeria where the virus was probably contracted from.
It can pass from human- to-human via droplets in the air, and by touching the skin of an infected individual, or touching objects contaminated by them.
Initial symptoms include fever, headache, aching muscles, backache, swollen lymph nodes, chills and exhaustion.
Officials from Public Health England said they were in the process of contacting people who sat near the Nigerian on the flight, who is being treated in "strict isolation" at the Royal Free Hospital in North London.
A rash can also develop, usually starting on the face before spreading to other parts of the body.
According to the World Health Organisation, Monkeypox is similar to human smallpox, which was eradicated in 1980, and is transferred from animals to humans. It eventually forms a scab which falls off.
Its experts are working closely with NHS colleagues "as a precautionary measure" and will be contacting people who might have been in close contact with the individual to provide information and health advice. There is no confirmation about whether the patient is a member of the military. This is the first time this infection has been diagnosed in the United Kingdom (UK). Most people recover within several weeks.
It is a rare disease caused by monkeypox virus, and has been reported mainly in central and west African countries.
The risk to the wider public is considered to be very low, PHE said.
Dr Nick Phin, deputy director of the National Infection Service at PHE, said: 'PHE and the NHS have well established and robust infection control procedures for dealing with cases of imported and infectious disease and these will be strictly followed to minimise the risk of transmission'.