Simon Lane said young students at Merridale Primary School in Pennfields, Wolverhampton, were left upset after discovering the building had been destroyed.
The wooden hut was used regularly by nursery and reception age pupils and was even supposed to double up as Santa's Grotto this year.
"It's just so depressing," Mr Lane said. "We've had the forest school for five or six years now and the nursery and reception pupils go every week.
"And now some vandals have set fire to it. It was also meant to be our grotto for Christmas - so it's really disappointing. The children are so upset."
The fire was started on Wednesday night but staff did not discover what had happened until the next morning.
Neighbours called the fire service after spotting smoke billowing from the site near Merridale Cemetery on Aspen Way.
"It was gutting really, to see that. What was a really lovely resource for our children has now gone, and it's so sad to see.
"The fact it was going to be Santa's Grotto too, it's really upsetting.
"When some of the children saw it – they didn't know it had burnt down before – it was quite traumatic for them.
"It's just mindless vandalism – the fact that these people have come and smashed something up without stealing anything, just for their own enjoyment. It's hard to understand."
"We do tend to get a lot of vandalism around here," Mr Lane added. "We can't really secure the back of the site properly.
"We back onto a cemetery, so people who want to get through can. But we're working with the police now to try and find a way of making our site more secure."
West Midlands Fire Service has confirmed the fire was started deliberately.
Matthew Smith, a spokesman for the service, said: "We were called at 9.36pm on Wednesday night and sent 10 firefighters – the fire was at a woodland educational structure at Merridale Primary School.
"It looks like it has been deliberately started."
West Midlands Police has been contacted for comment.
The school will be launching a crowdfunding campaign to build a new forest school for the children. Anyone interested in helping can call 01902 558760.