Almost 40,000 people have been to the art gallery since the exhibition was launched on September 21.
Around 1000 people a day are visiting and in a bid to cope with the large numbers Kelvingrove bosses have decided to open until 8pm on Friday, November 8. It will be only the second time the gallery has extended its hours since it reopened after a refurbishment in 2006.
The first major retrospective of Vettriano's work brings together more than 100 of his paintings belonging to private owners including American actor Jack Nicholson.
Anyone who wants to take advantage of the late night opening can pre-book tickets or simply turn up on the night.
Every visitor that evening will receive a complimentary limited edition Jack Vettriano poster.
Glasgow Life chairman Archie Graham said: "We are thrilled to host this exceptional retrospective of the career of Jack Vettriano.
"The tens of thousands of people who have taken in this wonderful exhibition are testament to the fact that the people of Glasgow and beyond are also thrilled the city is able to bring together some of the great treasurers from Jack's career.
"We are delighted to be able to open the museum later on November 8, giving the public another opportunity to enjoy the retrospective."
The only other time Kelvingrove has opened late was during an exhibition earlier this year called More Than A Game - How Scotland Shaped World Football.
It ran for five months this year and attracted 15,000 visitors - less than half the number the Vettriano exhibition has attracted in just six weeks.