A victim of fast-paced celebrity fashion, the company is in the process of what the directors called yesterday "an orderly wind down".
Described as the "Chanel of England", Miss Muir who died 12 years ago, was a favourite of the likes of Joanna Lumley, Dame Judi Dench and Lauren Bacall.
The spring/summer 2007 collection will be the last bearing her name and, when the doors of the shop in London's West End shut after Easter, it will bring a unique era of British streamlined style and understated sensuality to a close.
The company, which employs 25 people, recently celebrated its 40th anniversary with Jean Muir: Beyond Fashion, a lavishly illustrated book documenting the designer's extraordinary career. Yesterday, Harry Leuckert, Miss Muir's husband, who has run the company since her death from breast cancer in 1995 aged 66, said: "It is sad, but I believe this is the way Jean would have wanted it.
"I have, of course, had offers, but I do not want Jean's name to fall into the wrong hands and be mis-used. That would be horrendous and she would have hated it."
Mr Leuckert, 77, said sales in the Conduit Street store and the brand's remaining few outlets were satisfactory but "not enough to keep us going". "Basically, the Jean Muir label never quite recovered from the loss of its figurehead," he said.
He added: "I believe there is a virtue in quitting while we are ahead and keeping her name untarnished."
Miss Muir established her label in London in 1966. A pioneer of minimalism, she became renowned for her slinky dresses in black and navy silk jersey, which flowed around the body, the more revealing for what they were concealing.
She was revered in America, and in Paris she was known as la reine de la robe.
Her international legion of fans reads as a top-drawer line-up of women celebrated as much for their careers and intellects as their fame.
As well as Lumley, Dench and Bacall they included Dame Maggie Smith, Dr Miriam Stoppard, Charlotte Rampling, Julie Walters, Patricia Hodge and Joan Plowright.
They say husbands accompanying their wives at the Jean Muir store in Conduit Street, London, are amazed to be offered a Beck's beer and the day's newspapers to read while the all-important business of shopping for a wardrobe goes on.
It certainly does not seem the kind of service you might be offered in either the modernist Brit-brand shop, PPQ, on one side or the garish, rock'n'roll fashion emporium emblazoned with the slogan Voyage Directed by Rocky and Tatum, on the other.
Jean Muir, is, after all, an elegant anachronism in a celebrity-obssessed world; one which that world perhaps no longer deserves.
Harry Leuckert, for 12 years the keeper of the Jean Muir flame, reveals, almost apologetically, that he did once copyright the name Pure Muir for the first Jean Muir perfume - but never took it any further.
Perhaps it is for the best. Jean Muir abhorred the cult of branding; in fact, Joanna Lumley, her first house model, muse, close friend and loyal customer, cannot remember her wearing perfume. "She even hated the smell of oranges."
Jean Muir refused to call herself a fashion designer; by far preferring the word dressmaker, with its notions of craft and technique.
The collections, modelled in stately fashion to the music of American cabaret singer Bobby Short, stuck strictly to the Miss Muir line - a subdued palette of black, navy, chocolate and beige and then the clash of neon yellow, shocking pink or an abstract pop art motif.
It was the clash which astounded; very much like Miss Muir herself - rigorously disciplined, fiercely proud of her Celtic, Scots-northern roots, but luxuriating in being able to sketch in bed in her all-white "snow and ice" bedroom, furnished with 19th century Venetian cut glass sofa and chairs originally made for the Nizam of Hyderabad.
As Lumley remembered yesterday: "Jean Muir was the creative power, she was her clothes. Like Coco Chanel she embodied the personal style her label and her name represented, the two were inseparable. She was never a product."
The spring/summer 2007 collection is sure to become collector's items, just as the early dresses and coats are now sought after in cult vintage stores in London and Los Angeles.
Miss Muir would have liked the thought of her work being treasured. But she would have hated to think of it being translated into a 101 franchises. "I think it is brave to stop now," Lumley said. "It's a most graceful and elegant way to do it - discreetly, just like Jean herself."