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.
This year, Paraguay have lost away to Uruguay and Brazil and at home to Chile, picking up a solitary point in a 1-1 draw in Ecuador.
Paraguay have 24 points with four matches remaining, three points less than leaders Brazil and two behind Chile. Argentina are fourth with 22 points and Bolivia ninth with 12.
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.
Squad:
Goalkeepers: Justo Villar (Real Valladolid), Aldo Bobadilla (Independiente Medellin), Diego Barreto (Cerro Porteno)
Defenders: Julio Cesar Caceres (Boca Juniors), Denis Caniza (Nacional, Paraguay), Carlos Bonet (Olimpia), Dario Veron (Pumas UNAM), Paulo da Silva (Sunderland), Claudio Morel (Boca Juniors), Antolin Alcaraz (Club Bruges), Aureliano Torres (San Lorenzo), Marcos Caceres (Racing Club, Argentina), Miguel Angel Samudio (Libertad)
Midfielders: Enrique Vera (LDU Quito), Edgar Barreto (Atalanta), Cristian Riveros (Cruz Azul), Jonathan Santana (VfL Wolfsburg), Victor Caceres (Libertad), Osvaldo Martinez (Monterrey), Eduardo Ledesma (Lanus)
Forwards: Salvador Cabanas (America, Mexico), Nelson Haedo Valdez (Borussia Dortmund), Oscar Cardozo (Benfica), Edgar Benitez (Pachuca), Jorge Achucarro (Newell's Old Boys)
