The centre-back suffered the injury during Barcelona's 5-2 victory over Real Madrid in the Spanish Super Cup held in Saudi Arabia on Sunday.
According to a statement from Barcelona, "Tests conducted on Tuesday morning revealed that Martinez has a right hamstring injury. He is anticipated to be unavailable for approximately four weeks."
Ronald Araujo, who took Martinez's place during the match against Madrid, is likely to fill the void, amidst ongoing rumors regarding a possible transfer to Juventus.
At 33 years old, Martinez has established himself as a vital component of Barcelona's defense this season under coach Hansi Flick.
His absence will be felt in the team's final two Champions League group stage matches against Benfica and Atalanta, among other fixtures.