The 27-year-old Santa Cruz is suffering from a muscle pull from Saturday's 2-0 home defeat to English Premier League champions Manchester United, keeping him out of action for three weeks.
"It's a pity but I will not be able to play," said Santa Cruz. "The injury is causing me real problems."
The Paraguay squad, which meets Colombia in Bogota on Saturday and then hosts Peru in Asuncion four days later, started squad training on Monday.
Paraguay lead the ten-nation, South American South Africa 2010 qualifiers with 17 points ahead of a trio of nations on 13, Brazil, Argentina and Chile.