Martin Roth, Director of the V&A said: "We knew that Savage Beauty would be very popular, but the response has been even greater than we imagined."
He added: "It is not going on tour to other venues so our aim is to provide as many people as possible with the opportunity to see it by opening through the night for the last two weekends.
"This will be the first time we have opened the V&A around the clock and we certainly think it is an event worth getting out of bed for."
More than 345,000 people have visited the Alexander McQueen show, making it the most visited paid-for exhibition at the V&A in the last decade.
The museum revealed it had received 10,000 new members during the exhibition - with members gaining free entry - and its Friends of the V&A membership was now 75,000.
An earlier version the Savage Beauty retrospective took New York by storm when it opened in 2011 at the Metropolitan Museum of Art (Met).
London-born fashion designer Lee Alexander McQueen killed himself in 2010, at the age of 40.
