Workers in hazmat suits got onto the plane, which was due to fly from Stansted Airport to Pisa, and took the man and his mate off.
Once removed, flight attendants disinfected their seats and the overhead cabins they had used before the flight eventually took off, two hours behind schedule.
Footage filmed by a fellow passenger shows two people dressed in full hazmat gear talking to someone who is sat down.
A Ryanair spokesperson said: "A passenger who boarded a flight from London Stansted to Pisa on August 26, received a text message notification before departure that he had tested positive for Covid-19
"The passenger and his travel companion were immediately offloaded and taken to a Stansted Airport isolation area where they were assisted by local public health authorities
"There was little if any risk of Covid-19 transmission to other passengers or crew members as all of whom were also wearing face masks at all times.
"The aircraft departed for Pisa following a delay of 1 hour and 20 mins to allow for the empty seats and overhead cabin bins to be disinfected to comply with all UK health authority guidance. Ryanair apologises to all passengers for this short delay."
One passenger who was on the flight, told Sky News he saw a fire truck approaching the plane before two men hoped down and donned hazmats.
Fionn Murphy said: "At this point we started to feel a bit panicked, not knowing if the flight would be cancelled, or worse we'd been exposed to the virus.
