The Stoke midfielder suffered the injury in Friday's World Cup qualifier against Sweden at the Aviva Stadium.
Republic boss Giovanni Trapattoni has called up Hull midfielder Stephen Quinn as his replacement.
Trapattoni's side head to Vienna in desperate need of a victory following their 2-1 defeat to Sweden, a result that left them trailing in fourth place in Group C.
A Football Association of Ireland spokesman said: "Glenn Whelan has withdrawn from the Irish squad to face Austria in Ernst Happel Stadion, Vienna on Tuesday, September 10 with a hamstring injury following a scan this afternoon.
"Hull City's Stephen Quinn has been called up as a replacement, and will join
up with the squad in time to depart for Vienna tomorrow afternoon.
"Jon Walters also underwent a scan this afternoon on an ankle injury, and will
sit out training tomorrow as a precautionary measure, but is expected to be fit
for Tuesday's game."