It is believed a Nigerian naval officer travelled to the UK on a commercial fight after contracting the disease.
He stayed at a Royal Navy base in Cornwall while taking part in a training exercise before being confirmed to have the disease on Friday.
Public Health England has contacted passengers on the plane who were sat close to the man to warn they may have been exposed to the infection.
It is the first ever recorded case of monkeypox in the UK, Public Health England confirmed.
The victim was taken to hospital after he fell ill at the naval base.