Crews received a call to attend the Energy Recovery Facility in Dunbar at 2.36am on Tuesday.
The fire was still burning at around 7am, with two lines of hose being used against the flames, a Scottish Fire and Rescue Service (SFRS) spokesman said.
He also said 300 tonnes of waste was alight at the Viridor plant.
An hour later the SFRS issued a statement warning people that “large plume of smoke will be visible from a distance”.
It said: “Around 40 firefighters are currently at work tackling a large fire at an Energy Recovery Facility in Dunbar.
“SFRS mobilised a number of resources to the scene after the alarm was raised at 2.36am this morning.
“A large plume of smoke will be visible from a distance.”