In a statement the chef blamed the “extremely difficult decision” on “rising costs and challenging market conditions”, as well as the size and location of the site.
“We’ve had a wonderful seven years in Bristol and I am deeply saddened that we cannot find a way to continue trading here,” says Fearnley-Whittingstall.
“I have a strong personal connection to Bristol, having lived here just around the corner from the restaurant for most of the last four years. I very much hope that River Cottage will return to the city in the future."
River Cottage Kitchen Bristol will be open until 27 March.
The company hopes to offer staff alternate employment at its other sites, which include River Cottage Kitchens in Axminster and Winchester.
A River Cottage Kitchen also opened at Whipsnade Zoo in Bedfordshire in 2018.
Fearnley-Whittingstall founded the River Cottage HQ farm and cookery school in Devon, made famous on the Channel 4 series Escape to River Cottage, which he is planning to expand with the construction of a guesthouse and event spaces.