The airline said the problem started on Thursday morning when its network connecting internal and external systems began malfunctioning.
The cyberattack had delayed 24 domestic flights for more than 30 minutes, and the impact could expand later in the day, the airline said.
The Kyodo News Service reported the airline told police it might have been the victim of a distributed denial-of-service, or DDoS attack, in which networks are overwhelmed by data from multiple sources over a short period.
Ticket sales for both domestic and international fights scheduled for departure on Thursday were suspended temporarily.
Chief Cabinet Secretary Yoshimasa Hayashi told a regular news conference the transport ministry told the airline to hasten efforts to restore the system and to accommodate affected passengers.
Television footage showed many passengers at Tokyo's Haneda airport held up by the attack that hit the busy year-end holiday travel season.
Other Japanese airlines, including ANA Holdings, Skymark and Starflyer, were not affected.
Japan's main travel season is just picking up, as offices close from this weekend for the New Year holidays, the biggest celebration of the year, when millions of people travel back to their home towns from the cities.
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