The meeting between the First Minister and the head of the No campaign will be broadcast live on the BBC in the evening.
Preparations for the debate mean that the central hall in the gallery will also be cordoned off on Sunday, meaning the usual organ recital has been cancelled.
Kelvingrove will re-open as normal at 10am on Tuesday next week.
The debate will last 90 minutes and will be attended by 200 members of the public who will put the representatives of the opposing campaigns on the spot as they seek answers about the choice Scotland faces in September's referendum.
Glasgow Life chairman Archie Graham said: "It has been an extraordinary year for Glasgow which has seen some of our cultural landmarks shine on a global stage.
"Kelvingrove Art Gallery has played host to many historic occasions since it opened in 1901 and this is certain to be another ahead of next month's referendum.
"We are sorry for any disruption caused and hope customers can make alternative arrangements to visit one of our other museums or return to Kelvingrove when we reopen on Tuesday."