The owners of Dumbreck Riding School, one of only two in the city, cited "financial reasons" for the closure, which will be on September 16.
Gavin and Claire Bell said they had found it increasingly difficult to reconcile falling revenues and rising costs.
Lessons start at £12.50 for a half hour guided lesson for children and £25 for a one-hour hack.
The centre, based in Pollok Country Park, will continue as a "DIY" livery yard for horse owners.
All the school's ponies are being rehomed and the school said gift vouchers for lessons would be honoured until the closing date.
The city's last publicly owned riding school - Linn Park Equestrian Centre - closed in 2009 despite a campaign to keep it open.
Former and existing pupils of Dumbreck took to Facebook to express their sadness at the closure.
Sarah Scott said: "Such a shame! Most of my childhood was spent at Dumbreck, lots of great memories"
Carol Christie-Lunski said: "Dumbreck was the start of my love for horses. I now live in USA and have my own horses that I show and compete on.
"Thank you for all you have done over the years. I'm sure many tears will be shed."
Joyce Sherry said: "Very sad news, truly is the end of an era."
A statement on the riding school's Facebook page said: "We regret to announce that, due largely to financial reasons, Dumbreck Riding School will be compelled to close on September 16.
"Gift vouchers will be honoured until this date only.
"We have taken this decision with great reluctance, given the many years the riding school has been in our family, and a source of fun and fond memories for generations of children and adults.
"However, in the present economic climate we have found it increasingly difficult to reconcile falling revenues and rising costs.
"We thank you for your custom and understanding."
Dumbreck is one of only two riding schools in the city. The other is run by Glasgow Riding For The Disabled Association in Caldercuit Road, Summerston.