The restaurant's cleaners called the fire brigade after spotting the blaze in the kitchen. No-one was hurt in the incident, but the kitchen suffered fire and smoke damage.
East Sussex Fire & Rescue's crew commander Jon Lee said: “It is quite a big restaurant with a large kitchen and firefighters had to make their way through a heavily smoke-logged large industrial kitchen to reach the seat of the fire.
“The early intervention from cleaners and the closed kitchen door prevented the fire spreading to the rest of the restaurant."
In a statement Terre a Terre said it would remain close while work was carried out to repair the kitchen and that it had cancelled all reservations for the next seven days.
A spokesperson for the restaurant said owners Amanda Powley and Philip Taylor were 'slightly frazzled but as ever optimistic' and were hoping to re-open the restaurant as soon as they could.
Powley added: "[There is] huge relief that no one has been hurt, the emergency services have been wonderful and our customers, suppliers and staff have been hugely supportive and understanding - the Phoenix is a little damp but will rise."
Classically-trained chefs Powley and Taylor launched Terre a Terre in 1993 as a 30-cover Bring Your Own vegetarian restaurant. The restaurant has more than doubled in size since then and won a string of awards. It launched its first cookbook in 2009.