The All Black playmaker was replaced during the second half of the 20-13 derby win over the Hurricanes in Wellington on Friday.
The 26-year-old will undergo further tests on his ankle during the Crusaders' two-week hiatus, the Canterbury side taking a bye in round nine.
The Crusaders later revealed that further tests had ruled Carter out for at least six weeks.
A delay in recovery could threaten his availability for New Zealand's tests against Ireland and England in June.
Carter sustained the injury while making a tackle on a Hurricanes player during the second half. He was assisted from the field immediately and took no further part in the game.
"He will be unable to bear weight on the ankle during the initial stages of his recovery," Crusaders doctor Tony Page told official team website crusaders.co.nz.
Page said the injury was similar, but more acute, to the ankle strain which left scrum-half Andrew Ellis out of the early stages of the competition.
Ellis was originally expected to be sidelined for six weeks but recovered in half that time.
"Once the swelling has reduced, Dan will be reviewed and we will have a clearer picture of the likely timeline as to when he will be able to resume training," he added.
Carter is currently on leave, but will undergo further assessment next week.