Highgrove Beds in Liversedge ceased production after eight factory employees tested positive for coronavirus.
The Kirklees Council, the Health and Safety Executive and Public Health England are now working with the factory.
It comes after outbreaks in the Kober meat factory in Cleckheaton and in the Dura beds in Batley.
A statement from the Kirklees Council earlier this afternoon said, "Highgrove Beds – which was inspected last week by the Kirklees Council and set high standards for infection control procedures and practices – has made a decision to stop production for safety reasons and will be reopened, if this is certain. " so.
"All employees are now to be offered tests, and a mobile test unit is being set up on site.
"The company also works closely with the Kirklees Council and Public Health England so that those who have tested positive can be tracked and self-isolated by the NHS Test and Trace program.
"While the risk to residents of this outbreak is very low, everyone in Kirklees should continue to distance themselves socially, wash their hands regularly with soap and water for 20 seconds, and have them tested for symptoms.
"Find the latest pandemic safety advice here."
Councilor David Hall, Conservative Councilor for Liversedge and Gomersal, said: "It is encouraging that the Council, Public Health England and employers are working together to do the right thing on behalf of Kirklees residents.
"It will always be a problem if you get an outbreak, but I think Kirklees, like any other local authority, should be prepared to see quite a few isolated outbreaks over the next few months."
He urged people to continue to follow hand washing and social distance guidelines.
Colleague Michelle Grainger-Mead added: "It is worrying that we are seeing more and more of these localized outbreaks, particularly in the Kirklees region.
"At this stage, however, it is imperative that all companies continue to report these incidents and work closely with Council and government officials and follow the recommended guidelines.
"The last thing we want is for this type of outbreak to go unreported and for the virus to spread throughout the community.
"Thanks to the honesty and integrity of our local companies in Kirklees, we manage to keep the virus at bay and do everything we can to prevent it."
She added: "I just want to ask the local community to be vigilant, to follow the rules of social distancing and to continue to report these outbreaks.
"One point that is quite worrying is that many of the younger generation seem to think that the virus is gone and they are immune to it.
"It didn't and it isn't. Young people, though less likely to have symptoms of Covid-19, can still transmit the virus to their older and vulnerable relatives.
"The rules for social distancing are there for all of us and I urge everyone to take this into account as we move around our community."