Knead Pizza on Finewell Street received the rating after an inspection on April 25.
A spokesperson for the restaurant says it had previously never scored below a four in past inspections.
They say, as Knead Pizza is situated in the historic building of Prysten House, which is more than 500 years old, there have been "complications" which have been highlighted and works carried out immediately.
The owners say they are "grateful" to the hygiene inspector who gave them directions "as to where our efforts to improve the business should be focused". They say they believe they will achieve the ratings they were previously used to at the next inspection, which Knead Pizza is waiting for.
A spokesperson for Knead Pizza said: "Getting a zero is obviously gutting for any respectable restaurant, we've never had anything close to this in the past, only ever 4 or 5.
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