Style is Eternal, which showcases key items from his 50-year career, has been running at the Bowes Museum in County Durham since July.
It has been the most popular exhibition in the museum's history, attracting three time the usual visitor numbers.
The initial closing date of 25 October has now been extended to 8 November.
The show highlights how the designer revolutionised womenswear and includes dresses from the late 1950s which have never been seen in public before.
There have been 55,000 visitors to date, a figure which is expected to reach 70,000 by the time it closes.
Adrian Jenkins, Director of The Bowes Museum said:  "It has been a wonderful moment in the museum's history.
"The exhibition has dazzled visitors and informed us of Yves Saint Laurent's huge contribution to the world of fashion, evident in the way women dress every day."
The first major UK exhibition of the work of French designer Yves Saint Laurent has proved so popular that it is being extended.