The 29-year-old injured his knee for the Crusaders in early March and required an operation, only returning to the field in late May.
He went on to play all three British and Irish Lions Tests, as well as a protagonist's role in the Crusaders' Super Rugby triumph, but was rested from the All Blacks' two Bledisloe Cup Tests against Australia.
Characterising his knee niggle as a case of "old man syndrome" last week, Dagg went on to play just fewer than 50 minutes in Saturday's 39-22 win over Argentina.
But the issue appears more serious than Dagg intimated.
Hansen has not selected the 66-Test veteran for this weekend's clash with South Africa, and said Dagg's injury prognosis was poor.
But the exact time frame of his recovery remained unclear.
"We're getting more and more information on that and it doesn't look great at this stage. It looks like he's going to need some time away," Hansen said.
Props Owen Franks (Achilles) and Joe Moody (shoulder), and rookie fullback Jordie Barrett (shoulder) have all been ruled out for the rest of the season.
Hansen has plenty of options to replace Dagg, even if team vice-captain Ben Smith is on a sabbatical until next year's Super Rugby season.
Nehe Milner-Skudder will start on the right wing against the Springboks at North Harbour Stadium while Waisake Naholo is also in the squad and comfortable in the number 14 jersey.