Tulare County fire officials say the fire sparked north of Goshen on Avenue 328 around 9 am.
Firefighters say about 1,000 tons of hay was on fire.
Photos shared on the Tulare County Fire Department's social media showed flames ripping through the stack, sending a huge plume of smoke into the air.
Fire officials say crews were working to keep the fire contained to the barn.
The cause of the fire is under investigation.