Giggs injured his toe in Bilbao and then aggrevated the injury in training on Monday.
Defenders Mark Delaney, Richard Duffy and Rob Edwards had already been ruled out of the match in Graz with injury.
Sam Ricketts and Owain Tudur Jones are also missing because of Swansea's League One play-off final on Saturday.
With so many full-backs unavailable, Toshack has called up Crystal Palace's teenager Rhoys Wiggins to the squad for the first time.