The fire service advised local residents to close windows and doors, and for those in the area to avoid Priory Way to the A63 area.
It also stated that motorists should be mindful of a "large amount of smoke" in the area and on the surrounding roads.
Videos shared on social media show thick plumes of smoke billowing into the sky over residential areas on Wednesday afternoon (November 24), with many in the area reporting "explosions".
Humberside Fire & Rescue tweeted at 4.42pm: "We're currently in attendance at an incident in the Hessle area. We advise local residents to close windows and doors. Please avoid the Priory Way to A63 area and be mindful there is a large amount of smoke in the area and surrounding roads."
Humberside Police also warned members of the public to avoid the area.
A local resident living on Boothferry Road told Radio Humberside: "The smoke in the beginning it was so black, now it's changed. You could smell it, it affected my throat. I was stood looking through the window and the explosions vibrated through the floor."
Another said they were walking their dog and saw a huge plume of smoke billowing up "which "just filled the sky". He said "explosions" had set off car alarms, adding: "They were really loud bangs. There's a lot of debris, ash, coming down."
Grace Grant, 25, told the PA news agency that she heard explosions coming from the fire.
“It was huge, smoke could be seen from miles away. As I moved off, explosions were happening around every 10 seconds”, she said.
Buses have also been diverted due to the incident.
East Yorkshire Buses tweeted: "Due to an ongoing incident on Hull Road/Hessle Square. Service 57 & 66 can not currently serve Hessle Square. Service 66 will operate to Cottesmore Road before operating via the Darleys Roundabout and back onto Cottesmore Road. Service 57 will terminate at the fire station."