The former Liverpool forward was forced off after 20 minutes of Bayern Munich's 6-1 win over Werder Bremen on November 8.
Bayern coach Julian Nagelsmann said Mane had taken a painful blow to his "tibial plateau" and would have an X-ray to determine the extent of the damage.
A further scan was recommended in Qatar and the Senegalese Football Federation has now taken the decision to rule Mane out of the World Cup.
Team doctor Manuel Afonso told a press conference: "Unfortunately, today's MRI says his recovery has not been as encouraging as we had hoped and we have decided to declare Sadio Mane's withdrawal from the World Cup."
Mane is Senegal's record scorer and scored the decisive penalty as his country beat Egypt to win the Africa Cup of Nations earlier this year.
Senegal begin their World Cup campaign against the Netherlands on November 21 and also face hosts Qatar and Ecuador in Group A.