Morant had to be helped off the court in Friday's 121-110 win over the Oklahoma City Thunder after getting tangled with Lu Dort in the fourth quarter.
The 23-year-old is averaging 28.6 points and 7.1 assists per game this season for the Grizzlies, who are already without Desmond Bane, who will be re-evaluated in two to three weeks due to a Grade 2 sprain of his right big toe.
"After further evaluation, it was determined that Memphis Grizzlies guard Ja Morant suffered a Grade 1 sprain of his left ankle during the November 18 game against the Oklahoma City Thunder," the franchise announced on Saturday.
"Morant's return to play timeline will be week-to-week, and updates will be provided as appropriate."
Meanwhile, ESPN have reported that Philadelphia 76ers guard Tyrese Maxey will miss three to four weeks with a small fracture in his foot revealed by an MRI from Friday's 110-102 loss to the Milwaukee Bucks.