Jebi is the strongest typhoon to have hit Japan in 25 years, causing at least six deaths and 160 injuries.
Jebi, which made landfall in western areas of the country, brought heavy rain and winds of up to 172kmph.
Officials ordered more than a million people in affected areas to evacuate their homes amid warnings of high waves, flooding and mudslides.
"Customers are advised that due to typhoon Jebi, all flights into/out of Osaka Kansai International Airport on September 4 and 5 have been cancelled due to the airport closure and heavy flooding," the airline said.
"Customers connecting onto affected flights to Osaka will not be accepted at the original point of departure until further notice," the statement added.