The Well Pharmacy, in The Street in Brundall, has had to close temporarily on several occasions in recent months.
It has left people having to travel further afield to collect medication, with the village GP surgery only able to dispense medication in certain circumstances.
Health bosses say the problem stems from the site frequently not being able to secure a pharmacist, meaning it often has to rely on locum workers.
Jan Davis, who represents Brundall on Broadland Council, said: "It is clear this is extremely frustrating for people in the village, many of whom are elderly and struggle to get about easily.
"This has been a concern for quite some time now and there does not seem to be a solution in sight due to a lack of planning in making sure there are enough qualified pharmacists."
