Abdoulaye Sow said Senegal will have to cope without their best player for the start of the tournament and "not whine too much."
"We will have to rely on playing the first games without Sadio and win without Sadio because we have 25 players apart from Sadio," Sow said. "No one would have wanted it, but that's what's happened to us."
Sow didn't specify how many games Mane is expected to miss, and there has been no official word from Senegal or Bayern Munich.
Mane was injured a week ago in a Bundesliga game between Bayern and Werder Bremen. He was substituted in the 20th minute of Bayern's 6-1 win. Bayern said the two-time African player of the year has an injury to the head of the fibula bone in his lower right leg.
Most of Senegal's squad arrived in Qatar for the World Cup on Sunday without Mane. The team's first game in Qatar against the Netherlands is on Monday but Mane was still waiting for more tests by the Bayern medical team.
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Senegal, the reigning African champions, plays hosts Qatar four days after they face Netherlands. Their final game in Group A is against Ecuador on Nov. 29.
Mane was named in Senegal's 26-man World Cup squad last week by coach Aliou Cisse, who said at the time that Senegal were hopeful Mane might still be ready for the start of the tournament.
But Bayern coach Julian Nagelsmann had cast doubt Friday on Mane's participation when he said the player would be sidelined for at least another 10 days even before follow-up tests to determine the precise extent of the injury.
"It's obvious that Senegal would like him to play," Nagelsmann said. "But if he's in pain, he can't play. The medical things are more important than the sporting ones. That's the case with us and also with everyone else."
Senegal won their first major title at the African Cup in February, when Mane scored the winning penalty in a shootout to beat Egypt in the final. Mane also bagged the winning penalty in a playoff that sealed a place for Senegal in Qatar.