Raphinha was hurt during Brazil's 2-1 friendly defeat by France in the United States on Thursday.
In a statement, the Brazilian Football Confederation said that Raphinha and Roma full-back Wesley had both "felt pain in their right hamstrings during the match against France".
"On Friday, the players underwent tests that confirmed muscular injuries," the CBF added.
Barcelona released their own statement confirming the length of Raphinha's convalescence.
"The player is returning to Barcelona to begin the appropriate treatment. The estimated recovery time is five weeks," Barcelona said.
Raphinha is a key player for the Catalan giants, who will be without him for both legs of the tie against Diego Simeone's Atletico, at home on April 8 and then away on April 14.
The 29-year-old, who has scored 19 times this season for Barca, will also miss La Liga matches against Atletico, Espanyol, Celta Vigo and Getafe.
Barca will hope Raphinha is fit to play in the Clasico against Real Madrid on May 10, or a potential Champions League semi-final against Arsenal or Sporting Lisbon on April 29.
He should also be available for Brazil at the World Cup, which begins in Canada, Mexico and the United States on June 11.
