The former Liverpool player was injured during Monaco's 2-1 win in their French Cup tie against Auxerre on Sunday.
The 30-year-old was stretchered from the field of play with his face in his hands.
Minamino, who has 26 goals in 73 caps for the Samurai Blue, is one of the key men in coach Hajime Moriyasu's side.
Japan have been drawn in World Cup Group F alongside the Netherlands, Tunisia and a European play-off winner to be determined between Poland, Sweden, Ukraine and Albania.
The tournament in the United States, Canada and Mexico will run from June 11 to July 19.