The fire broke out at about 1.17pm at the factory on Ings Road Retail Park and thick black smoke is billowing from the building.
There are 20 engines battling the blaze from across West Yorkshire, using six breathing apparatus and a large jet.
Thick black smoke has descended over Wakefield and witnesses have described hearing 'explosions' from the fire.
A nearby resident, known as Yorkshire Dave on Twitter, said power had been cut to the neighbouring houses.
He added: "It's getting worse in Wakefield, explosions now at Speedibake."
Former MP Mary Creagh is working from an office in Wakefield and said: "The smoke is pouring out, the whole centre of Wakefield looks like nighttime.
"I visited the factory a couple of years ago and they have a big frying facility, as they make donuts.
"There is a lot of sirens and really huge flumes of thick black smoke."
Pictures show nearby Cineworld in 'lockdown' with firefighters keeping customers inside the building.
There are road closures in place across Wakefield and West Yorkshire Police have advised drivers to avoid the city centre.
A police spokesperson said: "We would ask all residents living in and around Westgate Retail Park in Wakefield to close their windows and doors.
"The wind is causing the smoke from the fire to blow into the city centre."