Grant, who was injured in Sunday's win over the Philadelphia Eagles, will require surgery to correct a torn ligament in his ankle that will leave him on crutches for 10 to 12 weeks, a source told ESPN NFL Insider Adam Schefter.
Grant is likely to fly to New York to visit a doctor for a second opinion.
FoxSports.com first reported that Grant would be put on injured reserve.
The Packers also placed former first-round pick Justin Harrell on injured reserve and signed running back Dimitri Nance and defensive end Jarius Wynn to fill their spots on the roster heading into Sunday's home game against Buffalo.
"When you lose a running back of Ryan's caliber, it's a big loss, but this is something we have to deal with and move forward from as a team," general manager Ted Thompson said in a statement. "Our medical people will do a great job with Justin and Ryan, and we expect each to make a full recovery from their injuries."
Packers coach Mike McCarthy said Monday that Grant's injury involved ligament damage.
More tests had been scheduled for Tuesday, and the results weren't encouraging enough to try to bring Grant back this season.
"Guess everyone has heard the news," Grant posted on his Twitter account. "Frustrating, disappointing, all the normal emotions."
Grant, who is in the third year of a four-year contract, was wearing a protective walking boot on his right foot after the injury and said after Sunday's game that his ankle was only sprained and not broken. On Tuesday, he said there was a chance he could return this season after surgery, but it would have been very late and put the Packers in a bind with their roster moving forward.
"It was more severe than initially thought during game," Grant tweeted. "But I just have to move forward and get it right. Anyone who knows me understands that my spirits WILL stay high."
The injuries come at two of the thinnest positions for the Packers, who have been tabbed as a favorite to reach the Super Bowl.
Jackson, a second-round pick out of Nebraska in 2007, played well in Grant's absence on Sunday. He rushed for 63 yards on 18 carries and caught two passes. Kuhn added a touchdown in the third quarter on Sunday. Jackson knew he would be the starter for at least a week on Monday, but didn't know the extent of Grant's injury.
"I started in '07, and [my family] just kept telling me, be patient, be patient, your time is coming. And now that it's here, I know my wife is just excited," Jackson said. "I'm telling her, let's just play the game. Let's continue to do what we did before I was the starter. Everything's going to work out."
Nance, who was signed off the Atlanta Falcons' practice squad, played four years at Arizona State, running for 1,934 yards and 19 touchdowns.
Harrell hurt his left knee in Sunday's victory at Philadelphia, yet another setback for the team's first-round pick in the 2007 draft who has played in only 13 regular-season games in his first three years after a series of back problems.
McCarthy had said Harrell would be placed on injured reserve. He is under contract through 2012.
"It's difficult when you lose players to injury. We felt like Justin was going to make a contribution to our team," Thompson said. "The timing of his injury and the way it occurred was unfortunate."
Wynn was the first of two sixth-round picks by Green Bay in 2009 and played in 11 games as a rookie last season. He was released by the Packers in the final roster cutdown earlier this month.
Information from The Associated Press was used in this report.