The 32-year-old has been struggling with a calf problem for much of the season and has only completed two of the Spanish champions' last eight matches.
The Spain international is set to miss the La Liga matches against Rayo Vallecano, Malaga and Espanyol.
But Xavi is targeting a return in time for the Copa del Rey final against Athletic Bilbao on May 25.
That is now Barcelona's only realistic chance of adding another trophy this campaign after seeing their hopes of a glorious season go up in smoke in the past week.
The Catalan giants slipped seven points behind Real Madrid when they were beaten at home on Saturday before being eliminated from the UEFA Champions League by Chelsea on Tuesday evening.
Barcelona have also confirmed that defender Gerard Pique will be unavailable for a week after suffering a blow to the head during a collision with his goalkeeper Victor Valdes on Tuesday.
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