The 33-year-old defensive midfielder suffered the injury in Bundesliga action against Bayern Munich last weekend and his club Eintracht Frankfurt said on Saturday he would require an operation.
Hasebe, an integral member of Vahid Halilhodzic's side, was injured when he collided with a goalpost while clearing a Thomas Muller shot off the line.
Japan are second in Asian third round qualifying Group B, tied on points with group leaders Saudi Arabia and one clear of Australia in third place.
The top two from the group receive spots in the finals in Russia in 2018 while the third-placed team can also qualify via two playoff rounds, the second against a CONCACAF team.
The Blue Samurai take on the UAE in Al Ain on Thursday and the Thais in Saitama five days later.
Japan lost 2-1 to the UAE at home in their opening match of the round and will be desperate to get their revenge in Al Ain to keep up the pace at the top of the group.
Halilhodzic named Hasebe in his squad for the matches on Thursday, when he was under the impression that his captain was back in training despite the injury.
"(He) is a very strong captain for us," the Bosnian told reporters. "Having a team without him in it is unthinkable."
Hasebe has won 104 caps for Japan and played in the 2010 and 2014 World Cups finals, the last two of five straight appearances at soccer's international showpiece for the Blue Samurai.
(Reporting by Nick Mulvenney in Sydney, editing by Andrew Both)
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