During September, Connacht have Magners League fixtures against the Ospreys (home), Edinburgh (away), Cardiff Blues (home) and Ulster (home).
Liam Bibo has also picked up a calf injury but he is expected to be back in action before too long.
Commenting on McCarthy's injury, Connacht coach Michael Bradley said: "He could be out for four weeks. We hope it might be less, but he is certain to miss the opening few games."
Connacht, who finished bottom of the league last season, are gunning for a strong start to the competition this month - especially with some of their opponents missing their international players for the opening run of games.
"We're playing four matches against sides that won't have their first choice players available to them on the basis of their Lions involvement," added Bradley.
"That should give us a great opportunity to get some points on the board and get off to a good start in the Magners League.
"We want to qualify for the Heineken Cup next season. We can do it by one of two ways, either by finishing in the top three in Ireland, or by winning the European Challenge Cup.
"It's a case of being realistic about what's available to us. We have a side that is quite young but maturing all the time in terms of game-time that they have had together."