Grant (right ankle) and Harrell (left knee) suffered injuries in Green Bay's 27-20 win over the Philadelphia Eagles in their season opener on Sunday.
The loss of Grant, who has rushed for more than 1,200 yards in each of the last two years, came as a particularly severe blow for the Packers.
"When you lose a running back of Ryan's caliber, it's a big loss," Packers general manager Ted Thompson said in a statement. "But this is something we have to deal with and move forward from as a team.
"We have confidence that our other players will step up and meet the challenge of these losses. Our medical people will do a great job with Justin and Ryan, and we expect each to make a full recovery from their injuries."
Green Bay, viewed as possible Super Bowl candidates with emerging quarterback Aaron Rodgers coming off a Pro-Bowl season, signed running back Dimitri Nance and defensive end Jarius Wynn to replace Grant and Harrell.
(Writing by Mark Lamport-Stokes in Los Angeles; Editing by Ed Osmond)