Lienert-Brown suffered the injury in the Chiefs loss to the Blues in Super Rugby Pacific at the weekend.
He suffered a similar injury on the All Blacks end of year tour last November.
The Chiefs say the 26-year-old is expected to return to rugby after approximately six months.
The Rugby Championship is scheduled to start in August, with proceeded by a three test series against Ireland in New Zealand in July.
Jack Goodhue returned to club rugby at the weekend, a year after he ruptured the ACL in his knee.