The Italian-themed chain will shut its outlet in Edinburgh’s Newhaven district on Pier Place.
The restaurants at Glasow Fort on the country’s west coast are also among the closures.
A total of 94 of Prezzo’s 300 outlets across the UK will shut.
Around 500 jobs are understood to be in the firing line, although the company has claimed many staff will be redeployed at other restaurants.
Edinburgh’s prominent North Bridge restaurant has been saved – at least for now.
Two outlets in Aberdeen and one in each of Livingston and St Andrews have also escaped the closures.
Prezzo, owned by private equity firm TPG Capital, secured the backing of creditors for Company Voluntary Arrangement (CVA) today.
The agreement will allow the Italian-themed chain to exit unprofitable branches and secure rent reductions.
The number of closures includes all 33 of its Tex-Mex themed Chimichanga outlets.
Prezzo, which worked with AlixPartners on the restructuring, employs 4,500 people.
The CVA proposal was backed by 88 per cent of the creditors, including landlords.
Prezzo boss Jon Hendry-Pickup said: “I would like to thank our creditors and landlords for supporting our transformation plan.
“While we continue to be profitable, the pressures on our industry have been well documented.
“Despite this being a tough decision, the support given today by our creditors shows that they believe we have the right approach to transforming Prezzo in the eyes of teams, customers and stakeholders.
“It has been a challenging time during the CVA process and I would like to thank our suppliers, colleagues and customers for their patience and support.”
The 94 restaurants identified for closure are likely to shut in April and May, Prezzo said.
Staff will be made aware of the exact dates as soon as they have been confirmed.
The announcement comes at a bleak time for the high street and the casual dining sector in particular.
This year has also seen burger chain Byron and Jamie’s Italian undertake CVAs as they come under increasing pressure from rising costs and falling consumer confidence.
As well as staff costs and lower footfall, the chains have been stung by the collapse in the pound, which has ramped up the cost of buying ingredients.
Soaring business rates, National Living Wage costs and the Apprenticeship Levy have also taken their toll.
News of Prezzo’s store closures come in a dismal first quarter for the UK high street, with Carpetright also announcing the prospect of closing outlets on Wednesday and Moss Bros and Mothercare in the doldrums.
Earlier this week, New Look agreed a restructuring plan with creditors that will see it shut 60 stores, resulting in the loss of up to 980 jobs.
Toys R Us is also closing all of its UK stores after going into administration.
An earlier version of this story stated Prezzo Silverburn would close. This was incorrect and we have updated the story after speaking with representatives of the store.