Nakarawa sustained the injury during the 30th minute in the 34-19 win over Dragons at Scotstoun last weekend.
Glasgow head coach Dave Rennue confirmed the news on the 31-year-old's injury.
"He injured his knee on the weekend," said Rennie.
"Generally you can get them back and going inside six weeks, so that's the plan."
Nakarawa rejoined Glasgow Warriors in 2020 after previously playing for them between 2013 and 2016. In between the two stints he played for Racing 92 but the French club terminated his contract for reporting to the club late from 2019 World Cup duty.