Fire crews from Featherstone, Pontefract, Castleford and Normanton were called to Farmer Copleys in Pontefract at 8.15pm yesterday as the fire took hold.
The farm, which also has a shop, cafe and restaurant and hosts regular festivals and community events, described the fire as "massive" on its Facebook page.
A post yesterday read: "OMG it’s all happening at the farm tonight. A massive barn fire. Basically Ben the farm manager has been mending his quad bike and it has burst into flames!"
The statement said no people or animals were hurt.
It added: "The firefighters have been amazing. Free food all round."
Since May 24, the farm has been hosting Paulos circus, which has not been affected by the blaze.
In a Facebook post this morning, staff at the farm said: "Just to quell any rumours, the shop, cafe and circus are open as normal today.
"It was the shearing barn and workshop that went up in flames. This is taped of and safe. We are just very happy no people or animals were harmed."
West Yorkshire Fire and Rescue Service said two hose reels and two large jets were used to extinguish the blaze