Unbeaten Walsh was involved in a car accident earlier this week and has been advised to rest for the next month.
The 26-year-old, a surprise pick as challenger despite winning all 13 of his fights, was due to meet Burns at the ExCeL London on December 15.
"I'm devastated 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"I have followed the advice of the doctors and withdrawn from the fight.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 title is my dream and this is just a setback and hope that I can get the opportunity to fight Burns again."
Burns, who was outstanding during his four-round demolition of Kevin Mitchell in December, will still headline the bill against a challenger yet to be named.
The 29-year-old Scot was upgraded from interim to full WBO champion after beating Michael Katsidis last November.