The show has drawn 37,000 visitors already and looks set to be the most popular exhibition ever at the museum.
Kelvingrove's record was set by the Glasgow Boys show in 2010, which attracted more than 120,000 visitors as well as wide critical acclaim.
Now the museum will, for the first time since 2006, stay open late, until 8pm, on November 8 to allow more people to see the show.
An average of 1000 people a day are seeing the show, which runs until February 23 next year.
Councillor Archie Grah-am, chairman of Glasgow Life, which runs the city's museums and galleries, 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 treasures from Jack's career."
Visitors can pre-book tickets for the late-opening or turn up on the night. Every visitor that evening will receive a complimentary Vettriano poster.