Santa Cruz was not included in a 25-man squad named by coach Gerardo Martino on Tuesday for the home matches in Asuncion against Bolivia on September 5 and Argentina four days later.
Martino will be looking for an improvement in his team after a slump in form caused them to drop from top to third in the South American group and not win any of their four qualifiers so far this year, all of which Santa Cruz missed.
"It's the worst moment we have gone through in the elimination series. We have gone four matches without winning, we've lost the last two and what was a calm run until last November has changed," the Argentine said.
"Now we are really playing the qualifying campaign we had always imagined from the beginning," Martino told a news conference.
Martino added that it was important for Paraguay, who are looking to reach their fourth World Cup in a row, to get a good result against the weaker Bolivians before facing Diego Maradona's Argentina.
The teams finishing in the top four places qualify for next year's finals in South Africa. The fifth-placed nation goes into a playoff with a team from the CONCACAF region.
Forwards: Salvador Cabanas (America, Mexico), Nelson Haedo Valdez (Borussia Dortmund), Oscar Cardozo (Benfica), Edgar Benitez (Pachuca), Jorge Achucarro (Newell's Old Boys)
