The Derby midfielder suffered an ankle injury during training this week and has withdrawn from Giovanni Trapattoni's squad.
Trapattoni, who named a 29-man squad at the weekend, will not call up a replacement for the 21-year-old.
A Football Association of Ireland statement said: "Jeff Hendrick has withdrawn from the Ireland squad to face Sweden and Austria next month after sustaining an ankle injury with his club Derby County.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 face the Swedes at the Aviva Stadium on September 6 before heading for Vienna four days later.
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.