Dagg missed selection for Saturday's Rugby Championship match with South Africa due to a long-standing knee injury and Hansen told reporters the prognosis "does not look great".
"We are getting more information on that," Hansen said in Auckland. "It doesn't look great at this stage.
"It looks like he might need some time away from the game but until I get more information it would be pointless to tell you how long or what is wrong."
The 29-year-old Dagg, who missed the two Rugby Championship clashes with Australia, was replaced last week against Argentina in the 49th minute after he aggravated the injury.
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.
(Reporting by Greg Stutchbury; Editing by Ian Ransom)
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