His statement came after he was named British designer of the year at the 2014 Elle Style Awards.
Kane, whose latest collection has been on show at London Fashion Week, said: "I think we're great united, stronger united, and that's it."
Talking about how his life has changed, he added: "People are always surprised I still have my Scottish accent. I'm very lucky, I have a great background and support."
Kane, 32, originally from Newarthill, is one of Scotland's top fashion designers. He has on course to open his first store this year in London's Mayfair. Last year French fashion giant Kering bought more than 50% of his business.
He is by no means the first Scottish celebrity name to put their head above the parapet and declare their opinion on Scottish independence. The Yes camp can count on support from Alan Cumming, Jack Vettriano, Irvine Welsh, Annie Lennox, and Kevin Bridges, while public opponents include Sir Alex Ferguson, Sharleen Spiteri, John Barrowman, Ewan McGregor, and Bobby Gillespie from Primal Scream.