The company sent a text-message to staff which read "Do not attempt to access site. Wait at your residence and a further update will be provided."
According to Energy News sources BP has ordered all staff onsite to take shelter indoors at the facility in an effort to protect workers onsite from the blaze.
This was confirmed by a BP spokesperson who said the company had implemented a take-shelter code.
At 7.58 AWST today the Department of Fire and Emergency Services (DFES) published a "Hazardous Materials" alert for the City of Kwinana.
"A fire in an industrial building is resulting in dangerous smoke in the vicinity. The building contains a mixture of products that are producing toxic fumes," the DFES said.
The DFES has now closed major roads leading to the refinery and the Tox Free facility.
There are currently 45 fire and rescue firefighters onsite.
In a statement to Energy News, BP said there were had currently been no impact to the Kwinana Refinery production operations.
"However, only safety critical and essential personnel will be permitted access to the refinery until the issue is resolved," a BP spokesperson said.
"We are working closely with emergency services and other authorities to monitor the situation. The safety of our employees is our priority."
Tox Free is a waste oil specialist which recycles and re-refines waste oil for reuse in lubricating and motor oils. The facility in Kwinana also processes oily water and disposes of other chemical wastes.