Photographs shared on social media showed the pavilion at Allison Park near Carmel Road fully ablaze.
The incident was reported on the Edinburgh Police North West Twitter page at around 9.44pm on Friday night.
With the building believed to contain asbestos, a public safety warning was issued by the emergency services and residents advised to stay indoors with their windows closed.
No casualties were reported, but images show that the building has been extensively damaged. A police cordon has been put in place around the site.
Police have been contacted to determine if there are any suspicious circumstances surrounding the fire.
Kevin Lang, Liberal Democrats councillor for the Almond Ward, condemned the fact the sports pavilion had lain empty following a previous blaze two years ago.
Speaking to the Evening News, Cllr Lang stressed the importance of clearing the site as soon as possible to prevent further issues: “The first fire required the relocation of a very popular playgroup and destroyed equipment.
“Allison Park is one of the few green spaces we have in Kirkliston and it should be thriving. We need to get this site cleared now so that we don’t have this shell potentially inviting more trouble.
Cllr Lang added: “It was a frightening episode for the residents last night with the asbestos warnings and it really shows how this building should not have been left in this state.”
The Allison Park pavilion closed for good following a suspicious fire in 2017.
No-one was harmed in the incident but the blaze caused significant damage to the interior and destroyed sporting equipment and a number of children’s toys.
A local children’s playgroup, which had been very popular in the area, was forced to find a new home as a result of the fire.