Rodgers was forced off the field early in the first quarter of his side's shock 27-20 defeat to the Chicago Bears on Monday night, and has since confirmed that he suffered a fracture of his left collarbone.
A return date has not yet been set for the 2011 NFL MVP, but McCarthy is confident that he will feature again this season having initially feared that he could miss the remainder of the campaign.
"I'm relieved, no doubt. With the new information that was given today, everybody felt better about it," McCarthy told reporters.
"How long? We don't have our hands around a timeline yet, but I know Aaron is very optimistic and he'll do everything he can to get back in a timely fashion."
Early reports have suggested that Rodgers could miss three weeks with the injury, which would see him sidelined for matches against the Philadelphia Eagles, New York Giants and Minnesota Vikings.