Both players are expected to be out of action for around three weeks as they recover from surgery to correct groin injuries.
The Republic face Georgia at home on 6 October and Moldova away on 9 October.
McCarthy, 25, missed the opening Group D qualifier against Serbia in Belgrade on 6 September, which ended 2-2.
McCarthy, who has featured twice for Everton this season, was included in manager Martin O'Neill's last squad in August but left the camp prior to the friendly game against Oman to receive treatment on his injury.
"Darron has had a similar operation to James McCarthy," said Everton manager Ronald Koeman on Monday.
"He will be out for about three weeks. It always takes around three or four weeks to recover from that surgery but he's doing well."
O'Neill names his squad for the qualifiers on Friday.
Everton midfielders James McCarthy and Darron Gibson are injury doubts for the Republic of Ireland's World Cup qualifying double-header next month.