The midfielder limped off in the dying stages of Tuesday's 2-0 Capital One Cup third-round victory over Sheffield Wednesday - his first match back from an ankle problem suffered in pre-season.
Cork was today seen at St Mary's in a leg brace and has confirmed via his Twitter account that he faces another stretch on the sidelines.
''Another 4-6 weeks, with my left knee,'' he said on the social media site.
''Lucks just not going my way this season. Could be worse, but was so close to getting back from the ankle.''
Saints manager Nigel Adkins confirmed the injury today.
''Jack Cork is not going to be available for the weekend or the next couple of weeks,'' he said.
''He picked up a knee injury the other night in the victory against Sheffield Wednesday so he is going to be in a brace for a couple of weeks.
''Who knows if four to six weeks is realistic? Listen, I know the diagnosis of it with the history I've got and the experience I've got of these injuries as well. We have got a good idea of what it is going to be.
''We have a great medical team here and they will work through the rehabilitation process in the diligent order.''