The council is reassuring those affected that money will not be taken from their account.
But a spokesperson said that until the issue is resolved payment should be by coin, by app, phone or online.
The problem is affecting all car parks that have "Flowbird" pay and display parking machines.
In Ludlow people took to social media to complain that they had had problems with more than one car park in the town.
A spokesperson for Shropshire Council said: "We’re aware of an ongoing issue that is affecting all card payments at all of our [Flowbird] pay and display parking machines, and our supplier is working hard to resolve things.
“We apologise for any inconvenience caused and we hope things will be back to normal very soon.
“For now, we ask people to pay for their parking by coin only, or by app, phone or online using MiPermit.
“If anyone has tried to pay by card at a machine they will find pending payments on their account but these will clear within a couple of days and the money will not be taken from their account.”
Shropshire Council said the situation did not impact Raven Meadows multi-storey car park in Shrewsbury.
