The event, believed to be the first of its kind in the world, is aimed at giving young people positive gay role models in sport and may even encourage high-profile stars to "come out".
The race through Kelvingrove Park on Friday, August 19, is the brainchild of Gay's Men Health, a Scottish charity. Tom Lusk, the community development manager for the charity, said: "We want to celebrate the sexual diversity that exists in our society and every individual's right to be unique."
Mr Lusk, 49, also believed the event could challenge homophobia in Scotland, saying: "What is clear to me and to many who work in the area is that the gay community does not feel welcomed or respected in a sporting environment. I think a change in perception is necessary and there has to be a role model for others to follow..
Mr Lusk emphasised that the Gay 5K was open to all runners, whatever their sexuality. "It is for the gay community, but also, of course, for everyone in society who who might shares principles and beliefs in a free and open society."
The event has been given the go-ahead by Glasgow District Council and Bellahouston Harriers will help in its organisation. Details of how to enter the race will be released next week.