Yorkshire Bank believes that this is the first time an artwork had been reproduced in this way.
The card, which features Jackson's watercolour 'Earth to Earth, life's pathway', was unveiled at an event in York on Tuesday September 29. It will be available for a limited period of time from November as the bank switches to Mastercard Debit.
Proceeds from the sale of limited edition signed prints of Jackson's artwork will help the bank's charity partner, Help the Hospices.
A Yorkshire Bank customer for more than 50 years, Jackson came up with the idea for the card after a discussion with his bank manager. He has previously backed a Yorkshire Bank painting competition for school children that will see their work used in a calendar to be sold in hospices.
Dean Cutbill, director for Yorkshire Bank, said: "We are extremely proud of the steps we have taken on corporate responsibility.
"We are continually reducing our carbon foot print, increasing the number of staff we have who volunteer and widening the scope of the local groups we support.
"One hundred and fifty years ago this bank was founded to support its local community, it is absolutely right that we continue that work."
"By embracing the ideals of our founder, Colonel Akroyd, and applying them in a modern context we are building a future for our business and the communities in which we operate."