One fire engine went to the scene after the alarm was raised at 11.45am on Sunday.
A second crew is being flown to the island by coastguard helicopter from Shetland, which lies to the north.
There are no reports of any injuries.
A fire service spokesman said: “The Scottish Fire and Rescue Service was alerted at 11.45am on Sunday to a report of a building fire on Fair Isle.
“Operations control mobilised one fire engine to the scene at Fair Isle Bird Observatory where crews are currently tackling the fire.”
Fair Isle is around halfway between Shetland and Orkney and has a permanent population of about 60 people.
The bird observatory was built in 2010 and is a popular spot for tourists, but it is believed that much of the building has been completely destroyed as the fire was still burning late on Sunday.