Grant left Sunday's victory over the Philadelphia Eagles with an ankle injury.
McCarthy described the nature of Grant's injury as "significant".
"I really do not have a timetable because we're still doing more testing," McCarthy said, according to the team's website.
Grant rushed for 45 yards on eight carries before his injury.
"They made the decision to take me out," Grant said. "They didn't want to make it worse than it was. Once I'd iced it for a while, they said 'We might as well put you in a boot."
Without Grant in the backfield, the Packers' only ball carriers are backup Brandon Jackson and fullback John Kuhn, who showed enough ability in the preseason to be considered the emergency halfback.
"As far as any roster moves, this is really preliminary," McCarthy said. "That's an ongoing conversation. Our personnel department, they're always grading tape and making lists and looking at different options."
The Packers also lost Justin Harrell for the season and the defensive lineman's future with the Green Bay Packers is in doubt.
Harrell sustained a season-ending anterior cruciate ligament injury in Sunday's victory at Philadelphia, the latest in a long line of significant injuries for the team's first-round pick in the 2007 draft.
Harrell has played in only 13 regular season games in his first three years, missing much of 2008 and all of last season with back problems. Still, he made the team's roster coming out of training camp.
"Justin's has had a tough go from a medical standpoint," McCarthy said Monday. "I've seen players in this league sometimes have injuries in bunches and then they're able to overcome them and go on to have a good career, and I was hoping Justin would fall into that category, and now he has another hurdle that he has to get over."
The team did not disclose which knee was injured, but McCarthy said Harrell will be placed on injured reserve, ending his season. He is under contract through the 2012 season.
Information from The Associated Press was used in this report.
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