Four fire engines from Ulverston, Barrow, Walney and Penrith were called to reports of a building fire on Urswick Road in Dalton-in-Furness.
Fire crews were called at 3:38am today, Sunday 7 July.
The barn was well alight on arrival.
A Cumbria Fire and Rescue Service spokesman said: “On arrival fire fighters quickly dealt with a fire involving a barn measuring twenty metres by thirty metres, the fire also involved an asbestos roof.
“Firefighters used two hose reel jets and two main jets.
“Fire crews remain at scene at this time.”