The large wooden shed at Devonshire Infant School in Smethwick was destroyed by the blaze which was started deliberately just before midnight on Saturday.
The shed contained tools for both adults and children including rakes and trowels, overalls and wellies for the children, kneeling pads, compost and other items of gardening equipment.
Deputy headteacher at the Auckland Road school, Sharon Gibson said: "The first I knew about was when I came in yesterday morning. I was so shocked, that someone would do this, just for fun.
"We had worked so hard to create this for the children, and only had volunteers from The Princes Trust in before half term to work on the allotment. The gardener has also lost all his log books in the fire which has records of all the childrens' work and the progress of the allotment."
The school held a special assembly today, where the teachers talked to the pupils about the fire. An emergency school council meeting was also being held this afternoon where the pupils and teachers will discuss the best way to move forward.
Mrs Gibson said: "We are not going to give up on the allotment because of this, and not let it get to us. We will now start looking at ways we can fundraise to replace the shed and the equipment."
Mrs Gibson said they had not had chance to work out how much the damage has cost them, but the shed was bought for £1,300 early last year, and there was a substantial amount of gardening equipment which has been destroyed in the blaze.
Police spokeswoman Deb Edmonds said they were called by the fire service just before midnight on Saturday.
She said: "The shed was completely destroyed in the blaze and it is believed to have been started deliberately. Unfortunately there is no CCTV which covers the area. We made door to door inquiries in the local area, and we are continuing with our investigations."
Sandwell school's boss Councillor Bob Badham said: "I think it's disgusting that someone should burn down the shed and destroy community items needed by pupils. It's very upsetting.
"The school will now have to replace these items. It's going to put a strain on budgets that are already under pressure."