People travelling to AFC Telford, which is being used as a jab hub, are allowed to use a nearby car park with the vehicle registration details collected by centre staff and volunteers on arrival.
However, vaccine centre operators Wellington Pharmacy said they were mystified by complaints that £100 fixed penalty notices were being issued and added that human error may be to blame for the mix-up.
Terry Rickard, 62, of Church Street, Hadley, and his wife Christine, 61, received a notice after leaving their car near the Whitehouse Hotel on March 3.
“We drove there and followed the yellow signs for the vaccine centre. When we pulled in a young lady wrote down our registration number in a big book.
“We assumed we were doing everything right. We were there for less than 30 minutes.
"We were very surprised to get a fixed penalty ticket. We were now wondering if other people have received them.
“We’re concerned that some older people will feel a bit worried if they get one and might pay it without querying it,” Mr Rickard said.
Vaccine site manager Kishan Mehta said: “We are a little mystified about why people are getting parking tickets.
"The car park is managed by ES Parking and we have a device to log the registration numbers of the vehicles belonging to patients coming for their vaccines so there shouldn’t be any issues.
“We suspect that human error may be the cause of the problem.”