The Men's Health Forum 10k has been held in the city's Bellahouston park for the last six years – but there are now fears the 2013 race will not go ahead.
This year's race raised £450,000 for good causes.
Race organisers have now sent out a desperate appeal to runners to help them fund the event in 2013 after the money they received from the Scottish Government was stopped.
Men's Health Forum Scotland are asking runners who took part in the past to help support next year's event, by donating £1 and getting 19 of their friends to do the same.
It is estimated that it will cost around £66,000 to stage the event.
Men's Health Forum Scotland, which works to promote healthy lifestyles and also conduct research into men's health issues, says its very existence could also be under threat without additional support.
Tim Street, the organisation's chairman, said: "We are trying to get corporate sponsorship but it is proving very difficult and, as it's not the biggest event, a lot of businesses don't want to know.
"We are also applying for grants.
"Without this money, we ourselves will struggle to keep going.
"We have a board of directors like any charity, but this could mean that we have to let our paid staff go."
According to the forum's research, around half the men who take part in each 10k have never entered a running event before, and many go on to take up regular exercise afterwards.
A Scottish Government spokesman said: "In 2010-11, we offered Men's Health Forum Scotland (MHFS) a time limited grant of £166,000 to fund core operating costs and advised them to identify alternative sources of support beyond 2010-11.
"We also offered MHFS a transitional grant in 2011-12 of £60,000 to cover operational costs while they continued to seek out other sources of funding.
"Much of the organisation's work is locally based and we do not believe it is appropriate for the Scottish Government to continue to cover core costs."
Almost 4000 runners took part in this year's race, which took place on Father's Day.
The race is the city's biggest men-only 10k.
The event, which started in 2006 with just 1400 runners, now attracts entrants from across the UK – as well as runners from around the world.