The fight with compatriot Murray was scheduled for London's O2 Arena on April 14 but will now take place on June 23.
Saunders has defended his title three times, most recently against David Lemieux in Canada in December.
"I felt my hand go during a session this week and sought medical advice immediately," he said.
"Unfortunately, I've been told that I can't punch anything for four weeks so we've been left with no choice but to withdraw from the date. My trainer Dominic Ingle will make sure I'm fit and prepared to put on another show on June 23rd."
(Reporting by Martyn Herman, editing by Ed Osmond)
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