Edinburgh Leisure is also set to reduce its community outreach programme designed to encourage people to take up sport.
Around 18,500 youngsters used the crche services in 2006/07, and parents today described the facilities as a "lifeline".
The cuts come as the Lib Dem/SNP administration prepares to reduce Edinburgh Leisure's annual grant of around 7.7 million.
Only two crches will remain open – at the Royal Commonwealth Pool and Ainslie Park Leisure Centre. The facilities at Drumbrae, Gracemount and Kirkliston leisure centres, Leith Victoria and Portobello swim centres and Craiglockhart Tennis and Sports Centre will all close. The annual Festival of Bowls tournament at Balgreen will also lose funding.
Edinburgh Leisure has 24 crche staff, and though most will be offered redeployment, the firm could not rule out compulsory redundancies.
The arms-length council firm said the decision was based on making maximum savings with the minimum disruption.
Nurse Lesley Barrow, from Longstone, said: "I first began going to Craiglockhart when my daughter was a child.
"I have used the facilities again recently as I look after my granddaughter and she goes to the crche while I'm at yoga.
"I'm really quite incensed that they're closing. In this day and age, when obesity and diabetes are on the rise, discouraging people from attending exercise classes is crazy."
Mother-of-two Mary Duff, 41, from Corstorphine, who uses the Drumbrae crche, added: "They're basically saying that if you're a full-time carer with a child, you're not entitled to exercise. They're closing a lifeline." Jeanne Liddell, a mother-of-two from Silverknowes, said she has now cancelled her Edinburgh Leisure membership. She added: "If they had asked people who use the facilities what they wanted, they would have found people actually wanted the crche extended."
Edinburgh Leisure has increased its income over the past ten years from 7m to 16m, as more people take up sport and other activities, but the crche services require a total subsidy of almost 290,000 – around 13 per customer per visit.
The firm said it was dealing with the "collective pressures" of ever-increasing utility bills, as well as less money from the council. Chief executive Keith Jackson said: "This has been an especially difficult time, particularly given the high regard in which these services, and the staff that deliver them, are held by our customers and by us."
Deputy council leader Steve Cardownie said: "Edinburgh Leisure's main job is to provide sports facilities – not childcare."
Edinburgh Leisure website