The 21-year-old Derby midfielder damaged an ankle in training with his club.
However, manager Giovanni Trapattoni, who named a 29-man squad at the weekend, will not call up a replacement.
A Football Association of Ireland statement said: "The Football Association of Ireland today confirmed that Jeff Hendrick has withdrawn from the Ireland squad to face Sweden and Austria next month after sustaining an ankle injury with his club Derby County.
"There are no plans at present to add a replacement."
The Republic of Ireland face the Swedes at the Aviva Stadium on 6 September before heading for Vienna four days later with the results of the two games likely to go a long way towards determining which of the three sides finishes second in the group behind current leaders Germany.