The image will be sold as a unique, digital non-fungible token (NFT) and a photographic print authenticated by the actor.
The auction will take place online at www.irisesoftheworld.org from midday CET/BST on 29 September until 6pm on 6 October.
Bardem, 53, rose to fame in the 1992 film Jamón Jamón, in which he played opposite a teenage Penélope Cruz.
Ojos del Mundo said they hoped to repeat the auction if this one was a success and that they were looking for an international sporting figure as their next donor.