Murphy sustained ligament damage during the National League loss to Dublin at Croke Park six weeks ago.
The full-forward is hoping to be fit for an Ulster quarter-final clash against Derry on June 16 if the county side overcomes Cavan.
Murphy did not require surgery on his injury but, despite an extensive rehabilitation programme, he won’t make the SFC opener.
The Glenswilly man had just returned to action in January after having surgery on a groin injury.
“We will bring Michael back only when he is ready, no sooner,” said Rory.