Catherine's in Broseley and Much Wenlock will close their doors on Saturday - unless new bakers or delivery drivers can be found - leaving nine part-time staff out of work and two high street shop units empty.
The business as a whole will continue trading.
Muriel Powers who runs Catherine's said: "We have struggled now for the last 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."
The Broseley and Much Wenlock branches have both been there for 20 years. If a baker and a delivery driver can be found in short order, the branches could be saved.
Broseley councillor Caroline Bagnall said: "Local people are devastated on hearing the news that the Broseley bakery shop is to close.
"Catherine's Bakery is not just a bread shop - it is a social hub and a much needed service for the community. Customers stand and chat to each other and catch up on the local news.
"I am very concerned about the loss of local jobs but also about the fact that Broseley will be without a bakers shop for the first time in living memory."
Councillor Bagnall added an impassioned plea to anyone willing to take on the job to ensure that the branches can be saved.