The Scotland full-back sustained the damage in the warm-up before last month's win over Australia.
Hooker Fraser Brown will also miss out after picking up a head knock in the same game.
"Stuart is out this weekend," Murray said of Hogg. "Fraser will probably be another week or so."
Murray added: "The medics will see how Stuart's recovery is - immediately after injury it's hard to put a time on it, so they'll see how he goes over the next week, then they can tell.
"The job is to get him on the park as quick as we can, but at the same time make sure we're managing it.
"Fraser has had a few injuries over a period of time, so we're cautious we don't bring guys back too quickly. We're looking for Fraser to get back through his return-to-play protocols within the week, so he should be back playing very quickly."
Both trained on Monday and if one is fit it would avert the scenario of James Malcolm, 23, being the only fit senior hooker at the club's disposal.