Chelsea striker Torres has once again been left out for games against Finland and France, with Puyol also missing out.
Torres scored the winning goal as his club reached the Europa League quarter-finals at the expense of Steaua Bucharest on Thursday night but also missed a penalty and remains short of his best.
Instead, Vicente Del Bosque will rely on Barcelona's David Villa and Pedro and Sevilla pair Alvaro Negredo and Jesus Navas for his forward positions.
Puyol captained Spain while winning his 100th cap in the friendly win over Uruguay last month but the veteran defender is not required for the double header.
Real Madrid goalkeeper Iker Casillas is injured, meaning Manchester United's de Gea returns to the senior squad in search of a first cap - though the presence of Victor Valdes and Jose Reina make that a tough ask.
Torres' club-mate Cesar Azpilicueta and Malaga midfielder Isco are both retained after making their international bows against Uruguay.
Swansea's Michu continues to be left out, having been told by Del Bosque ahead of the Uruguay match that he was unlucky not to be called up.
Although the squad features just two recognised centre-forwards - Villa and Negredo - Del Bosque refuted suggestions it was a negative selection.
"I believe in the centre-forwards and we have brought two that are sufficient for us because we have other alternatives in attack such as Pedro, Silva and (Juan) Mata," he said. "Nobody can doubt that we are an offensive team."
Del Bosque confirmed he had spoken to Puyol before leaving him out, adding: "I have had contact with him but he still walks with inconvenience. He wanted to come but we prefer not to bring him if he is struggling with his condition."
Squad: V Valdes (Barcelona), J Reina (Liverpool), D de Gea (Man Utd), A Arbeloa (Real Madrid), R Albiol (Real Madrid), S Ramos (Real Madrid), C Azpilicueta (Chelsea), G Pique (Barcelona), I Monreal (Arsenal), J Alba (Barcelona), Xabi Alonso (Real Madrid), Xavi (Barcelona), A Iniesta (Barcelona), C Fabregas (Barcelona), S Busquets (Barcelona),S Cazorla (Arsenal), J Garcia (Man City), Isco (Malaga), D Villa,(Barcelona), D Silva (Man City), Pedro (Barcelona), J Mata (Chelsea), A Negredo (Sevilla), J Navas (Sevilla).