Forty-nine employees at CBS Packaging in West Bromwich,have tested positive for Covid-19 - more than a third of the 117 workforce.
The outbreak was first reported by health officials on Friday evening.
On Saturday, Sandwell Council said there were 22 confirmed cases at the factory, with a further 15 employees showing symptoms.
The firm, on Brandon Way, will remain shut for 14 days in line with the incubation period for Covid-19.
The decision to close was taken by company bosses to prevent a further outbreak in the wider community.
A spike in cases has been seen in neighbouring Smethwick over recent weeks, with an urgent warning issued by public health officials.
Meanwhile West Brom fans who celebrated the club's promotion to the Premier League outside The Hawthorns have been urged to avoid anyone who is vunerable to Covid-19.
A council spokesman said the factory is "at the centre of a major coronavirus outbreak" in the borough.
Staff will be instructed to self-isolate at home for 14 days while public health teams will monitor their conditions.
Sandwell Council’s director of public health, Dr Lisa McNally, said: "CBS bosses have taken the decision to voluntarily close because they are as determined as we are to get on top of this outbreak.
"The company has co-operated with public health partners and assure us they are doing everything they can to comply with the advice and measures recommended.
"It’s now very important that all CBS staff members self-isolate at home. This will help prevent anyone else becoming ill.
"We would like to appeal to all businesses to contact us straight away if they have two or more cases of COVID-19 in their workplace.
"If we act early we can help minimise the impact on the employees and the business."
To contact Sandwell's public health team, email PHCovid19_Enquiries@sandwell.gov.uk