The Scotland international needs an operation on a torn hip muscle and will be out of action for six months.
"Ally has suffered a tear in a muscle in his hip and requires an operation," said Edinburgh head coach Rob Moffat.
"It means he will be out of action for six months and so will not be available for selection for the Six Nations.
"Ally was involved down in Bath and could have played again this week - in fact, he really wanted to play. But the club decided he should undergo surgery as soon as possible."
Hogg has played in all bar one of Edinburgh's eight Magners League fixtures so far this term, starting six matches and coming on as a replacement in another.
The 26-year-old has become a key member of the Edinburgh squad since making his league debut back in the 2002/03 season.
He has currently made 92 Magners League appearances and had been hoping to break the 100 barrier later on this season as second-placed Edinburgh look to secure a play-off berth.
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