He made his competitive return a month ago as Glasgow Warriors defeated Ulster 13-12 in the PRO12, kicking two penalties and a conversion in the victory at Ravenhill.
Hogg then started the following week's PRO12 clash against Leinster but was replaced midway through the second half after injuring his wrist, and has not featured since.
He has now undergone surgery and is expected to be out for several weeks with Scotland head coach Johnson preparing to look elsewhere for the autumn internationals.
Scotland face Japan, South Africa and Australia next month and Johnson said:"Are we counting Hoggy out of the Autumn Tests? Yeah, probably.
"There is a chance that he might make a game but that is unlikely. However, this is just a chance to blood someone else."