The former Manchester United man sustained a foot problem in the Catalans' 3-2 Champions League win over Spartak Moscow on Wednesday and will be out of action for a minimum of a fortnight, while the veteran is also sidelined.
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However, Xavi has little doubt that Barca will be just fine without the Spain internationals.
"All of the players who have picked up injuries are important. Puyol and Pique, without a doubt are very important, but the team is big enough to cope with their absences," Xavi was quoted as saying on his club's official website.
"It’s clear that it would be good to get them back before the Clasico, but we have a good team. [Sergio] Busquets, [Alex] Song, who played a good game, [Javier] Mascherano... all of them can play in the centre-back position.
"We’re focusing on Saturday’s match. Before the Clasico there are two more league games and another Champions League fixture."
Barcelona resume La Liga action on Sunday when they host Granada.