The 58 cases have been confirmed at Magna Specialist Confectioners, based on Stafford Park.
Staff at St Georges Sports & Social Club have also tested positive for coronavirus, and the club on Church Street has closed as a result.
The news came ahead of Telford and Wrekin being put into Tier 2 of the coronavirus restrictions from Saturday.
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The Covid-19 infection rate has been rising sharply in Telford and Wrekin in recent weeks.
The borough's average infection rate was 221.3 cases per 100,000 people in the seven days to October 25, compared to 154.0 the week before.
In comparison, the infection rate in the Shropshire Council area was 125.3 cases per 100,000 people in the week to October 25 and 84.5 the week before.
And as restrictions are altered for regions across the country, the Government is now considering implementing a new national lockdown for England from as early as next week.
Becky McHale, spokeswoman for Magna, said: "Since cases started rising in the community, we’ve seen 58 people report positive tests, information we share weekly with all our staff.
"We also operate a very thorough independent tracing system that enables us to quickly instruct close contacts to self-isolate. This is predominantly driven by car sharing and home contact.
"We’ve worked closely with the Telford & Wrekin Health Protection Hub and Public Health England (PHE) who are aware of the extensive preparations we made over the last seven months.
Latest infection rates across the region
The latest rolling seven-day infection rate of Covid-19 by local authority area, compared to the previous week.
The figures are for the seven days to October 26, with data for the most recent four days (October 27-30) excluded as it is incomplete and does not reflect the true number of cases.
The rate is expressed as the number of new cases per 100,000 people.
From left to right, it reads: name of local authority; rate of new cases in the seven days to October 26; number (in brackets) of new cases recorded in the seven days to October 26; rate of new cases in the seven days to October 19; number (in brackets) of new cases recorded in the seven days to October 19.
South Staffordshire 401.1 (451), 237.5 (267)
Cannock Chase 343.4 (346), 230.2 (232)
Walsall 336.3 (960), 235.0 (671)
Sandwell 317.9 (1044), 223.5 (734)
Stoke-on-Trent 315.9 (810), 221.6 (568)
Birmingham 276.4 (3156), 240.6 (2747)
Dudley 260.6 (838), 163.9 (527)
Wolverhampton 251.0 (661), 197.8 (521)
Stafford 243.3 (334), 162.4 (223)
Lichfield 234.8 (246), 164.2 (172)
Solihull 229.2 (496), 225.5 (488)
Telford and Wrekin 219.6 (395), 168.5 (303)
Shropshire 135.5 (438), 87.3 (282)
"They’ve pronounced themselves pleased with the depth of this work, and with the outstanding commitment of our staff to support each other and the business.
"With the rapid growth of cases in the community we expect to be continuing this fight for the long term and making sure that we can continue to operate the business safely.
A spokesman from Telford & Wrekin Council confirmed the authority was aware of the 58 cases at Magna.
He said: "As a precaution, affected work bubbles, including those car sharing and who live together have been asked to self isolate. The remainder of the business continues to operate and there is no risk to anyone else.
"The company is working closely with Telford & Wrekin Council’s Health Protection Hub which continues to monitor the situation.”
Meanwhile a statement from owners of the sports & social club said: "We regret to inform you that we have both tested positive for Covid-19 and are required to self-isolate.
"Unfortunately, this means that the Sports & Social Club will stay closed this coming weekend and will remain so until further notice.
"We are sorry for this inconvenience to you, but it is absolutely necessary to ensure the safety of both our staff and all of you and we hope to be welcoming you back quite soon."