The blaze, which happened just after 10pm last night, has left the River Cottage team at the chef's headquarters in Axminster, Devon, "shocked and upset".
Fearnley-Whittingstall, who is away filming, is yet to find out about the fire, a spokesman said.
The cause of the blaze is unknown.
Emergency services, including the police and fire crews, went to the scene after the single-storey building caught fire.
Devon and Somerset Fire and Rescue Service said eight fire engines and 80 firefighters attended the farm after receiving calls to a commercial kitchen on fire.
The fire was brought under control after nearly three hours and there were no injuries.
A spokesman for River Cottage said: "Late last night a serious fire severely damaged the main barn at River Cottage Park Farm headquarters in Axminster.
"Thankfully, no people, or animals, were hurt.
"The River Cottage team are dealing with the damage today and are shocked and upset.
"Hugh Fearnley-Whittingstall is away on a long-distance filming trip and will be informed as soon as he can be contacted.
"The River Cottage team would like to say a big thank you to the fire brigade, who were on the scene quickly and worked hard to contain the fire."
A spokesman for the fire service said: "We received calls to a commercial kitchen on fire.
"One fire appliance from Colyton and one fire appliance from Axminster attended with Watch Commander Richards in charge.
"Upon arrival, fire crews requested a further three fire appliances from Seaton, Lyme Regis in Dorset, and Honiton; a compressed air foam systems appliance from Chard in Somerset; together with the incident support unit and a supporting appliance from Exmouth and the water bowser from Danes Castle, Exeter.
"A hazardous materials and environmental pollution officer and fire investigation officer was also mobilised to this incident.
"The single-storey building was well alight, measuring 30 metres by six metres, used as a commercial kitchen."
Members of the Salvation Army also attended the scene to provide catering for those affected by the fire and members of the emergency services.
The River Cottage Canteen and Deli at Axminster was unaffected and is open today, a spokesman said.
But the cookery school courses at Park Farm will not be running in the short term.
"Anyone booked on a course will be contacted by the River Cottage events team as soon as possible," a spokesman said.
The roof of the cookery school kitchen, in a barn at the farm, has been completely destroyed by the fire, with much of the wood charred and blackened.
Fearnley-Whittingstall, a chef, writer, broadcaster and campaigner, moved into the original River Cottage in Dorset in 1998 to start growing and rearing food of his own.
In 2006 the headquarters moved into the farm near the Devon and Dorset border.
Based in Axminster, it is the base for running courses and events in line with the chef's commitment to ethically-produced food.
Fearnley-Whittingstall gained fame following his River Cottage TV series which led to the publication of The River Cottage Cookbook.
No-one lives permanently at the farm and the alarm was only raised by a gardener who was staying overnight in a flat in the farmhouse while working there.
River Cottage managing director Rob Love praised firefighters and said the 17th century barn was "well gone" by the time he arrived at 10.30pm.
"As you can see, it was a very sad sight this morning," he said.
"We are all very upset here at River Cottage that a beautiful barn is gone. We have spent a lot of time and effort to get this barn restored.
"We are just glad that nobody was hurt - we are just thinking how lucky we are."
He said Fearnley-Whittingstall was out of radio range, filming in the Southern Ocean, and they were trying to contact him.
The River Cottage website says of the events barn: "A beautifully restored threshing barn, with its oak floor and large windows, (it) is a glorious space at any time of the year.
"Of course the River Cottage kitchen team never disappoint, cooking up wonderful celebratory dinners using the very best local produce."
Devon and Somerset Fire and Rescue Service said the barn also houses a cooking school and contains around 10 ovens, each connected to individual gas cylinders, which were involved in the fire.
Work was continuing at the farm this afternoon, with workmen trying to restore electricity to the site.
Fire service investigator Mike Burrows said it was too early to speculate on what caused the blaze.
He added that firefighters had faced a difficult task.
"On arrival access was difficult due to it being down a narrow and steep lane. Another problem was access to adequate water supplies.
"When the crews arrived here the building was already suffering from a well-developed fire and we can see the result here as it has spread through the building and it is severely damaged."
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