Cobb, who is Green Bay's leading receiver this season with 29 catches, suffered a suspected fractured fibula when he was hit in the right leg by Baltimore Ravens safety Matt Elam during Sunday's match between the two sides.
"James, my understanding is he may have a chance. Randall does not have a chance this week. Randall will be multiple weeks," ESPN quotes McCarthy as saying.
Outside linebacker Nick Perry was also hurt during the match, although McCarthy admitted that he was surprised by that injury as he was able to return to the game in the second half.
"Nick Perry was a bit of a surprise to me. I didn't expect that. Obviously James and Randall, [we] saw the injuries in the game. You just hope for good news there," McCarthy added.
Sunday's win leaves the Packers third in the NFC North, although they have played a fewer game than the Detroit Lions and Chicago Bears, both of whom have a 4-2 record.