The blaze began on Friday morning in an art gallery in the centre of the city before spreading to the nearby Royal Clarence Hotel.
The hotel has stood on the same spot for 300 years and survived German bombers during World War II.
There are no reported injuries but the front of the hotel was badly damaged.The fire service said: "Fire crews are still at the scene working hard to get the fire under control.
"Residents are asked to consider their travel arrangements around the city centre as road closures may still be in place."
Around 120 firefighters from across Devon were at Cathedral Yard on Friday, where the blaze affected a block of buildings.
It is not known how or where the fire started.
A hotel spokeswoman said on Friday: "Following the morning's fire, all our guests and staff were evacuated and all are safe and accounted for."