Mama's & Leonies, on Norfolk Street, is being sold as a going concern after owners John and Catherine Hall decided to call it a day.
The restaurant, close to the Crucible and Lyceum theatres, has been established for more than 52 years and has attracted a host of stars over the years.
Maggie Smith, Kenneth Branagh, Steve Coogan and Dennis Waterman are just a few of the famous actors to have dined at the restaurant, where the menus say it was the first pizzeria in South Yorkshire.
Mama’s, which opened in 1968, is popular with snooker stars such as John Parrott and Stephen Hendry. The BBC has also interviewed players such as Steve Davis and Jimmy White in the restaurant.
The sale price is not being made public but owner John, aged 57, did say offers would need to be more than £250,000.
He added: “We want to retire and do a bit with our lives. It is time pass the baton on to someone else.”
His wife Catherine, 58, started working in the restaurant as a part-time waitress at 19. The Halls bought the restaurant, which can seat 78 diners, in 2005. It is set out over three floors with ground floor and first floor seating area and second floor staff room.
Catherine said: “It is a Sheffield institution. We are not shutting down, it is a going concern and we want the staff to be looked after.”
It is for sale on businessforsale.com and the listing says: “This is an incredibly well known, famous - even legendary - business.”
It adds: “Surely one of the finest businesses of this type that we have ever had the privilege of representing in our more than 20-year trading history, it is incredibly rare for such a well known and desirable business to be offered for sale in the open marketplace.”
The premises are held on a 12-year lease from 2016 with a rent payable of £3,750 per calendar month. Enquiries via businessforsale.com only.