ABP Foods in Cahir says the case was confirmed on Friday, and that all close contacts of the worker are self isolating and will undergo testing.
It is the second time a case has been confirmed at a plant in the county, after an outbreak at a mushroom plant in Golden last week.
Independent TD Mattie McGrath says the latest outbreak is a worry: "It is a concern, Cahir isn't all that far from Golden as you know in South Tipperary.
"I do appreciate the HSE are dealing with the mushroom plant, have dealt with it pretty swiftly, and I hope that this was detected earlier on, people are isolating so hopefully it can be contained to these two locations."
Operations at the Walsh Mushrooms Golden Ltd plant were suspended last week after one member of staff was diagnosed with Covid-19 while in self-isolation, with subsequent testing of close contacts resulting in further positive tests.
Tipperary lockdown
As all 170 of the plant’s staff underwent testing over the weekend to assess if the virus had spread, a local councillor warned that Tipperary could be placed into a localised lockdown by Monday if the outbreak was not contained.
Fine Gael councillor Michael Fitzgerald said on Saturday that “the worst-case scenario, the HSE people told me yesterday evening, is by Monday evening Tipperary could be closed down.”
"Let's hope in the next 48 hours the results will be good and it won't come to that.”
The results of the weekend testing at the mushroom plant are yet to be announced, with the company reporting 11 workers testing positive for Covid-19 out of around 20 tests on Friday.
In a statement on Friday evening, Walsh Mushrooms Golden Ltd said the cases were the plant’s first incidence of the disease.
“As a business we have stringent measures in place to control Covid-19 since March and we have had no incidence of Covid-19 up to this point,” it said.
“We are working with the HSE and all relevant authorities assisting in contact tracing and testing of all staff. We will use the opportunity to deep clean the plant during the temporary closure. Essential maintenance will continue at the facility.”