Branches of Catherine's in both Broseley and Much Wenlock shut on Saturday as bosses struggled to find bakers and delivery drivers.
Broseley councillor Caroline Bagnall said: "There is real sadness in Broseley at the closure of our lovely bakery. It was well used and such an important part of our community.
"One of the great things about our town is that we have a proper, traditional High Street.
"The loss of the bakery shop will have a knock on effect on other businesses. It is so important that we do all we can to restore this essential service to Broseley."
Last week Muriel Powers, who runs Catherine's, said the business had struggled for staff for 18 months.
"We haven't got enough bakers or delivery drivers. We need at least one more baker, but we can't get the staff," she said.