The fire, at Speedibake, on Westgate Retail Park, was first reported at around 1.15pm yesterday.
At peak, more than 140 firefighters were on the scene, with crews from Wakefield, Ossett, Normanton, Rothwell, Hunslet, Cleckheaton, Garforth, Dewsbury and Morley in attendance.
Photos and videos from the scene show thick clouds of dark smoke covering the city, while witnesses reported hearing 'explosions' from the scene.
There were also concerns that the building may have contained asbestos, though the fire service have now confirmed that this is not the case.
Nobody was injured in the blaze, which is now under control, but crews are expected to remain on site for most of Sunday and Monday.
A number of residents were evacuated, but were invited to return home at around 8.30pm last night.
The Ridings Shopping Centre, which closed during the fire but is open as usual today, has also offered free parking to those who were forced to abandon their cars overnight.
A number of bus services have been diverted as a result of the fire, according to West Yorkshire Metro.
An update on their website reads: "102 Outbound Diverting via college -Batley Road left at lights Flanshaw school, Flanshaw Lane - across at lights - back on route.
"Inbound right at lights - Dewsbury Road. Left at St Michaels Alverthorpe Road - right at Red Lion into town.
"105 Diverting via college - Batley Road - on route visa versa.
"117 Operating as a 107 through retail park - right on to Denby Dale Road - Right onto Thornes Road to Gill Syke flats - George a green back on route Flanshaw lights - Visa versa.
"126 127 services will be diverting from Horbury Road via Thornes Road and Denby Dale Road (128 Route) in both directions until further notice.
"212 212A Diverting from Alvertorpe Rd via Batley Rd and Wakefield college in both directions.
"268 terminating at St Micheals church due to services can go in but have no way out to pick up the route."
It is also reported that the A642 Westgate End, which runs close to the retail park, remains closed this afternoon.
Westgate Retail Park is open as usual, with the exception of Mecca Bingo, which will remain closed today (Sunday, February 2).
Wakefield MP Imran Ahmad-Khan also offered his thoughts to those affected by the fire.
He said: "I have been in frequent communication with Associated British Foods (ABF) that operates the Speedibake bakery in Wakefield. The MD of Speedibake is onsite now assessing the impact of the fire and seeing to the wellbeing of their employees.
"I have sent via David Webster (Director of Communications of ABF) a message of support and an offer of my assistance to help ensure the recovery process for all affected by this dreadful fire, especially the employees who have lost their place of work, is as swift as possible."