The 30-year-old suffered the injury while playing in Monaco's 2-1 win over Auxerre in the French Cup on Sunday.
"Our midfielder Takumi Minamino suffered an injury to his left knee," Monaco said in a statement on Monday.
"Medical examinations revealed a rupture of the anterior cruciate ligament."
ACL injuries typically rule players out for six to nine months, meaning Minamino is unlikely to recover in time for the World Cup, which will take place in the United States, Canada and Mexico from June 11th to July 19th.
Japan are in Group F of the World Cup, where they will face the Netherlands, Tunisia and a playoff winner. Their opening match is set for June 14th against the Dutch in Dallas.
Minamino's injury is a massive blow for Japan, with the former Liverpool player having made 73 appearances and scored 26 goals for the Samurai Blue.
His absence will also impact Monaco's season, with the French side ninth in Ligue 1 and set to face Spain's Real Madrid and Italy's Juventus in the Champions League group stage next month.