While Tesco hasn't said how many customers could have been affected by the fault at the 180-space car park in Ludlow town centre, it says it happened between March 11 and 24.
Fuming Tesco customer John Newman said he had received two penalty charge notices, one for parking at the Station Drive car park on March 13, and another time on March 20. On both occasions the notices were for £70 a time, or a reduced rate of £40.
The car park normally allows for customers to park there for two hours free of charge as long as tickets are obtained from the tills on checkout and they are used to validate in a machine before drivers leave the car park. Car number plates are registered on an automatic number plate recognition system.
"It has made me quite ill with the stress," said Mr Newman, aged 58, of Ludlow. "The Tesco people told me that they have had hundreds of customers affected.
"I am sure people have been paying the fines because there has been nothing I have seen in the store or in the car park to inform people of the error.
"The customer services lady was helpful and apologetic, and she had a list of hundreds of codes that she went through to find mine."
Mr Newman said the episodes had caused him unneeded stress.
"I had suffered a stroke and a bleed on the brain - not due to this - and I need to lead a quiet life," said Mr Newman, who has been a Tesco customer for many years.
"All Tesco has to do is write a letter to tell people. I bet hundreds of people have paid it."
A spokesperson for the Hertfordshire-based supermarket giant said: "There was a fault with the car park monitoring system at our Ludlow Superstore between the 11th and 24th March which meant that parking fines may have been incorrectly issued."
But the spokesperson added that all fines "issued in this period have been automatically cancelled and any parking charges paid have been refunded."
The company spokesperson added that Tesco is "really sorry for any inconvenience caused.”
The company says any customers who remain concerned that they have been incorrectly issued a parking charge should "contact the store and they will arrange for this to be cancelled."