Promoter Frank Warren confirmed that the bout between the pair, scheduled for December 15 in London, has been cancelled, with a replacement fighter to be announced.
Commonwealth junior lightweight champion Walsh, from Rochdale, injured his back in a crash earlier this week and has been advised by doctors to rest without training for a month.
"I'm devastated at the moment that I'm not going to be challenging Burns for the world title," Walsh said. "I have followed the advice of the doctors and withdrawn from the fight. The doctors have said hopefully I'll be able to resume training in four weeks.
"To fight for the world is my dream and this is just a setback and hope that I can get the opportunity to fight Burns again. I wish Burns all the best in his title defence and all the other lads on the show."
Burns will still headline the card at the Excel Arena in London's Docklands with a new opponent to be named soon.
It will be the Scot's third defence of his title.