The AC Milan midfielder injured his left calf muscle in the friendly loss to Mexico.
Enrique Vera and Lucas Barrios scored first-half goals to help Paraguay beat Greece 2-0.
Barrios, who plays for German club Borussia Dortmund, received his Paraguay passport just a few weeks ago.
Paraguay have been regular participants on world football's biggest stage over the last two decades.
Ivory Coast wasted a two-goal lead to draw 2-2 with Paraguay in a friendly.
Roque Santa Cruz is pleased that he is recovering well and will be fully fit till the time Wolrd Cup starts.
Surgeon who operated the player said his condition was critical but stable.
Paraguay book their place in South Africa while Argentina's chances fade.
England, Brazil and Argentina will be in action in World Cup qualifiers.
The baby, born 16 weeks prematurely, was presumed dead by docs.
Brazil steered closer towards the 2010 World Cup after edging Paraguay 2-1.
Argentina will now face Peru in the quarter-final.
Argentina moved into the quarter-finals of the Copa America.
Swede Freddie Ljungberg grabbed a priceless late goal to grab a 1-0 Group B win that saw them through to Round two.
England needed an own goal by Paraguay captain Carlos Gamarra to grind out a 1-0 victory in Saturday's Group B opener.
Peter Crouch will lineup up alongside Michael Owen in attack while Roque Santa Cruz has been called in by Paraguay.