Scotland team doctor James Robson said: "Phil sustained the injury in non-contact training yesterday. His rehabilitation starts now. He will have to undergo surgery in due course to repair the knee ligaments but the Edinburgh and Scotland medical teams will be working to deliver him ready to be considered for selection for the Rugby World Cup squad next year.
"I have seen Phil this morning and there are many examples of players returning to full international duty having sustained this kind of injury. From our own national squad Jason White and Nathan Hines have both recovered to play a full part in international rugby after ACL damage.
Edinburgh head coach Rob Moffat said: "It's desperately bad luck for Phil who has just played his 100th Magners League game for the club and is a key player for us. Clearly, we wish him a speedy recovery."
Godman's injury means David Blair is promoted from the bench to the starting XV for Friday's Magners League match against Leinster at Murrayfield (kick-off 7.05pm).
Tom Brown, last season's Scotland under-20 full-back, is enlisted to the bench and should he be called into match action would be making his Magners League debut.
Phil Godman, who won his 23rd and most recent Scotland cap in last season's Calcutta Cup draw against England, said: "I have to focus on my rehabilitation and target being available to go to the World Cup, which is a massive ambition for me."
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