Thirteen windows were smashed in the overnight attack on the Four Winds Inspiration Centre in Inverleith Park.
It is the latest blow to the charity which earlier this year announced it could no longer afford to run the Tree Fest.
Police are now examining CCTV footage of the attack which they hope will identify the vandals.
Project director Carole Fraser discovered the damage when she arrived at work on Tuesday morning.
"I realised something was amiss as soon as I came in because I saw the broken windows – our warehouse is an old greenhouse, which used to be a horticultural warehouse for the council. I felt really nervous as to what else we were going to find.
"They'd been into the toilet blocks and left the hot water running all night, and they'd been playing papier mache, so it was quite a mess.
"There was broken glass inside and outside. The council have a playbus parked nearby and they'd gone into that and set the fire extinguishers off as well, so they made a real mess in there too."
CCTV cameras were installed at the centre, which hosts classes ranging from paper making to stone carving, after a previous run of attacks, but the charity still faces a repair bill running into hundreds of pounds.
Ms Fraser said: "It's come as a bit of a blow because we're having a hard time financially. We're under pressure.
"These kids have no idea the impact of what their messing about has done. They think they can get away with doing whatever they want. We've worked hard over the years to try and make it nice, and then people come in and trash it."
She pledged that craft classes would continue at the centre, despite the set-back: "It will strengthen our resolve to carry on."
A police spokesman confirmed that the damage had been done between 8pm and 9pm on Monday, and said that anyone who was in the area at the time and noticed any suspicious activity should contact police immediately on 0131-311 3131, or call Crimestoppers in confidence on 0800-555 111.