Scotland wing Graham set to undergo season-ending groin surgery
The 26-year-old, joint third on Scotland's all-time try-scoring list with 24 from 39 Tests, had hoped to return from a quadricep problem in time for last week's game at home to England.
But he will now miss the entire Six Nations for the second year in a row.
"We really feel for Darcy because he is a player that puts his heart and soul into rugby," said Edinburgh coach Sean Everitt, who added that Graham would be out of action for up to four months.
"He loves playing for this club while he is a proud Scotsman who takes great pride in representing his country.
"We've got every confidence Darcy will work his way back from next week's surgery with the same drive and determination with which he trains and plays."
Graham scored five tries at the World Cup but suffered a hip injury in the final pool game against Ireland on October 7th.
He made his Edinburgh comeback in December but managed just four appearances before suffering the quadricep problem.
Glasgow centre Sione Tuipulotu is likely to miss the rest of the Six Nations after suffering a knee injury during the 30-21 Calcutta Cup win over England at Murrayfield.
Scotland, who have won two out of their three Six Nations games this season, continue their Championship campaign against Italy in Rome on March 9th.
