To receive the voucher, shoppers just need a minimum £5 spend on fuel.
The offer runs until Friday July 15, with vouchers to be redeemed by Sunday, July 31.
An Asda spokesperson said: “Asda is trialling the voucher initiative to the help support customers with the rising cost of living increases, after recent Asda research showed 58 per cent of customers are doing fewer, larger shops to save on fuel and 51 per cent are combining grocery shopping with other errands to keep driving costs down.”
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To redeem the limited time offer, customers are asked to show their fuel receipt to a checkout operator or a self-checkout host.
Once verified, the £5 discount will be applied to any shop of over £40.