Bhutan welcomed nearly 60,000 tourists between January and August this year, earning the nation $13.5m in revenue from the SDF
The airport, located to the west of London, operates at full capacity meaning it struggles to fit in its full schedule when weather conditions mean aircraft need to leave longer gaps on the runway.
"Some passengers may experience disruption to their journeys today," Heathrow Airport said in a statement on Monday. "Passengers should check their flight status with their airline before coming to the airport."
The British government gave Heathrow Airport permission to add a third runway last October but it is not due to be built until 2025.
Gatwick Airport, the country's second busiest airport to the south of London, said it had cancelled one flight.