It comes as Shropshire’s director of Public Health warned Shropshire was on the brink of having further restrictions imposed.
Meanwhile, the neighbouring Telford & Wrekin borough is expected to be moved up from Tier 1 into Tier 2 of the government's coronavirus regulations on Thursday.
All positive cases at Bridgnorth Aluminium are self-isolating for at least 10 days and contacts are isolating for 14 days.
The metal manufacturer, based off Old Worcester Road, is working with Shropshire Council and Public Health England (PHE) Midlands to manage the situation.
A spokesperson for Bridgnorth Aluminium said: “We confirm that 19 employees from our site have tested positive and are now self-isolating.
“PHE and Shropshire Council have been informed and we would like to stress that our procedures for dealing with Covid-19 follow best practice as set down by the Health and Safety Executive.
“The health, safety and wellbeing of our staff is our number one priority, and Bridgnorth Aluminium Ltd has introduced strong Covid-secure measures across the site.”
Rachel Robinson, Shropshire’s director of Public Health, confirmed the cases and said the county was "on the brink" of further restrictions.
She said: “We have been made aware of positive cases of Covid-19 at Bridgnorth Aluminium Ltd. We are working closely with the business and PHE to help limit any further potential spread.
"All positive cases are self-isolating for at least 10 days, with contacts isolating for 14 days, as per national guidance.
“We are now at a critical point in our battle against Covid-19. We are on the brink of having further restrictions being placed upon us here in Shropshire.
"That’s why we are urging everyone to follow the measures designed to keep everyone safe – particularly around observing the rule of six, limiting your social contacts, observing social distancing, frequent hand washing, and wearing face coverings in enclosed public areas, including public transport.”
For local advice and support during the pandemic, call Shropshire Council’s Covid-19 Helpline on 03456789028 or visit shropshire.gov.uk/coronavirus