Vandals gained entry to the grounds of Lauriston Castle late on Sunday evening and set light to the shelter within the estate.
Images have emerged that show the burnt-out shell of the gazebo, which stood at the top of a flight of steps in the Japanese garden.
The attack on the wooden structure is the latest in a spree of vandalism incidents at Lauriston Castle that includes damage to saplings, fencing and a number of garden ornaments.
Concerned local David Baker, whose late wife Frances worked on the estate for a number of years, says he holds council officials partly accountable for their failure in fixing faulty CCTV cameras in the area.
Mr Baker said: “I came across the burnt-out gazebo on Monday. It was clear an arsonist had completely destroyed it – an act that must have taken considerable time and effort.
"Over many years the garden has been used out of hours by people drinking, taking drugs and committing vandalism. While there are CCTV cameras in the area, they have no been operational for many years.
"Police resources have been wasted by the irresponsible behaviour of officials.”
Liberal Democrat councillor Kevin Lang, who serves the Almond ward, bemoaned the loss of the gazebo and called for a full review of security within the grounds of Lauriston Castle.
He said: “It is heart-breaking to see this kind of vandalism. The grounds at Lauriston Castle and the Japanese garden in particular are popular and peaceful places for families to enjoy. It’s terrible to see it left in such a state.
“Going forward, there needs to be a full review of the security of the grounds, perhaps with improved CCTV, so we can try and prevent this kind of mindless destruction from happening again”.
Scottish Conservative councillor Graham Hutchison is also calling on the council to take urgent action and prevent future incidents of vandalism.
He said: “The burning down of the gazebo in the Japanese Garden is the latest in a deeply concerning series of anti-social behaviour, vandalism and arson incidents in the grounds of Lauriston Castle and across Davidson’s Mains and Silverknowes.
“I have led a working group of local residents and other stakeholders over the past couple of years seeking to address issues of anti-social behaviour around Lauriston Castle and the council must now take urgent action to make the grounds and the artefacts contained therein more secure.”
A spokesperson for Police Scotland said officers were treating the incident as deliberate and have made an appeal for information.
The spokesperson said: "We received a report relating to a fire within the grounds of Lauriston Castle in Edinburgh around 10:15pm on Sunday, February 7.
"The fire was extinguished by the Scottish Fire and Rescue Service and nobody was injured.
"It is being treated as deliberate and enquiries are ongoing."
In a statement, a City of Edinburgh Council spokesperson said: “It’s extremely disappointing that someone vandalised and destroyed the Japanese Garden pavilion in this way.
"Police investigations are under way and we’d urge anyone with information to come forward."