Shoppers have said they are 'appalled' at the changes, with some saying they will boycott the store.
A petition calling on Tesco to scrap the changes set up by Samvarta Bandyopadhyay, the operator of Seacroft Post Office, has reached almost 800 signatures.
Tesco said it had it introduced the four hour limit on free parking for customers of Seacroft Green Shopping Centre to stop people using it as a park-and-ride.
But the land is leased from Leeds City Council, leading some who have signed the petition to accuse Tesco of setting up a 'money making scheme'.
-> Leeds man who suffered a brain injury in a horrific car accident hasn’t let it stop him writing a book about travelling the worldMotorists have also been fined for leaving the car park to use nearby services, such as the post office and Seacroft Community Hub.
The fact that the Post Office logo is still on the shopping centre sign has only added to the confusion.
In one case, an 89-year-old was fined for leaving the car park to go to the post office.
Many who have used the car park in this way for many years have been stunned to receive fines of £60, rising to £100 if not paid within 28 days or appealed, from UK Parking Control.
Mr Bandyopadhyay wrote in his petition: "Tesco Extra has got a huge advantage of being a supermarket adjacent to many important public buildings, including a college, a library, a post office.
"For years all these thrived supplementing each other's needs.
"The whole idea of transferring this public land from Leeds City Council to private hands was meant for developing the Seacroft area, not to impose penalties and fines against people who tend to use all the services offered in this area.
"Though the adjacent buildings have got limited parking, it seems ridiculous for people to move around with their cars.
"A fair usage policy and time restriction would have been enough for using the car park."
-> The 11 philanthropists who made their mark on LeedsLocal councillors David Jenkins, Katie Dye and Paul Drinkwater are calling on Tesco to reconsider the charge and Leeds East MP Richard Burgon has written to Tesco CEO Dave Lewis, demanding an end to the 'unfair and unnecessary' charges.
Coun David Jenkins called it a 'serious injustice'.
“We understand that Tesco want to keep spaces free for their customers, but they have used a hammer to crack a nut." he said. "The simple four hour time restriction does solve the problem of commuters parking there all day and potentially use the park as a park and ride facility.
“We are calling on them to think again and come up with a scheme that doesn’t penalise people who rely on the vital services accessed from the car park. We are also asking for the cancellation of all fines previously issued."
-> Inmates at HMP Leeds are tending to birds in a 'Chicken Wing'In response to customer feedback, Tesco said it had introduced a grace period of 30 minutes for those leaving the car park to use other services.
A Tesco spokesman said: “The car park at our Seacroft Extra store has a four hour limit on free parking for customers using the shops on Seacroft Green Shopping Centre. This was introduced to ensure there was enough parking for customers as non-customers were using the car park and travelling elsewhere.
“Fines will be cancelled for car park users who can show they have been customers at any of the stores at the centre and have kept to the four limit.
“Following feedback from customers we instructed parking wardens to allow a grace period for those users leaving the centre to use the neighbouring post office and other services. We would be happy to have further discussions with council representatives about this issue.”