Garstang Quality Meats, who run a meat stall inside the market, has confirmed that one of their team has contracted the virus.
It has reassured customers that its staff member is "well", but said it would have to keep the stall closed until October 30.
The team did not say whether any other staff members or traders inside the market had been asked to self-isolate.
A spokesman for Garstang Quality Meats said: "We are sorry to announce that as a precaution we have decided to close the Butchers until Friday, October 30, after seeking government advice due to a confirmed case of Covid 19.
"Please be reassured that the staff member in question is well, however we must do the right thing to safeguard our much valued customers.
"We hope you all understand and are so sorry for any inconvenience this decision may cause.
"We will keep you all updated and look forward to commencing business as usual on Friday, October 30."
The closure of the indoor market has affected a number of traders, with stalls selling cheeses, cakes, and sweets among those forced to stay closed today.
Garstang Town Trust, who run the market, have been approached for comment.
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