At the moment Morrisons customers collect points every time they shop. They earn five points for every £1 they spent, and once 5,000 points are collected they get a £5 discount voucher for their next shop.
These points will stop being awarded on May 10, and customers have until August 9 to use up all their existing points. After that they will no longer work.
From May 10, money-off coupons will be available via the Morrisons More app, which allows customers to scan barcodes when they get to the tills.
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Those without a smartphone can still store coupons on their Morrisons More card.
The new system aims to be more personalised, and sees shoppers earn money-off vouchers via the app.
It will also mean Morrisons can stop producing the plastic More cards, in a bid to become more environmentally friendly.
A Morrisons spokesperson said: “With Morrisons More, we are always listening to our valued customers, taking feedback on how we can improve the experience.
"What we've heard is that you'd like your rewards to be immediate, including discounts and money off your next shop.
"We also learned that you want to give back to your local community and to support environmental causes by going paper and plastic free wherever possible."
However, many shoppers have criticised the move and vocalised concerns about signing up for the new app.
One customer tweeted: “In order to take part I have to either download an app to my smart phone or go online.
“I don't want an app on my phone & I don't have time to keep going online to look for the deals. No good to me think I'll shop elsewhere!”
And one expressed concerns about those uncomfortable with technology being left behind: “Morrisons changing their “More” card, where point are accumulated and result in £5 vouchers for spending in store, to a scan app for smartphones.
"There’s a crossover but eventually it will be device only. Kick in the teeth for those without smart phones.”