Residents have been urged to avoid the area while fire crews try to bring the flames under control.
There are currently a dozen fire engines at the scene in Mill Street East, Savile Town.
Water is being pumped from the nearby canal to help extinguish the blaze.
West Yorkshire Fire and Rescue Service tweeted: “We currently have 12 fire engines & specialist units in attendance at a fire at an industrial unit in Saville Town #Dewsbury.
“All persons are accounted for.
“Please avoid travelling through the area.”
Kirklees Council said: “Local residents within the vicinity of the fire on Mill Street East in Dewsbury, particularly Chickenley and Earlsheaton residents, please keep doors and windows closed.
“There is no access to Mill Street East, Dewsbury, at this time.”
A number of people reported on social media having heard a “massive explosion” before the industrial unit burst into flames at around 5pm on Friday.
One Twitter user said: “There was a massive explosion in Dewsbury. Black smoke everywhere!”
Another wrote: “Somethings blowing up in Dewsbury.”
One man said: “I’m sat here a couple of miles away and heard a crescendo of loud banging, which I initially thought was a lorry carrying loose metal nearby. Looking outside after it got extremely loud, smoke was billowing in the horizon from the industrial estates near Mill Hill East.”
Plumes of smoke could also be seen from the motorway, with one person tweeting: “Saw the massive plume of black smoke from the M1. Hope no one was hurt!”
Ayah Alfawaris, 32, from Leeds who was visiting the area for the first time, said: “As we got to Dewsbury there was heavy traffic so we got out of the Uber and started walking to our destination.
“We saw at least four ambulances and three fire brigades on one street with some police cars. They started blocking off the roads and diverting traffic.
“The fire did seem to get bigger with time and I was a bit scared it was going to get closer to where we were.
“Firemen came with a truck to pump water out of the canal next to the pub. The manager gave them a crate of beer for later which was nice.