There was no impact on flight safety, it said.
JAL said the problem started on Thursday morning when the company's network connecting internal and external systems began malfunctioning.
The airline said it was able to identify the cause as an attack intended to overwhelm the network system with massive transmissions of data.
Such attacks flood a system or network with traffic until the target cannot respond or crashes.
The attack did not involve a virus or cause any customer data leaks, JAL said.
It said that as of late morning, the cyberattack had delayed 24 domestic flights for more than 30 minutes.
Experts have repeatedly raised concerns about the vulnerability of Japan's cybersecurity, especially as the country steps up its defence capabilities and works more closely with the United States and other partners with much tighter cyber defences.
Japan has taken steps but experts say more work is needed.
In June, Japan's space agency said it had suffered a series of cyberattacks since 2023, though sensitive information related to rockets, satellites and defence was not affected.
It was investigating to take preventive measures.
In 2023, a cyberattack paralysed operations at a container terminal at a port in the city of Nagoya for three days.
JAL's ticket sales for both domestic and international fights scheduled for departure on Thursday were suspended temporarily but resumed several hours later.
Chief Cabinet Secretary Yoshimasa Hayashi told a regular news conference on Thursday the transport ministry told JAL to hasten efforts to restore the system and to accommodate affected passengers.
Other Japanese airlines, including ANA Holdings, Skymark and Starflyer, were not affected.
Television footage showed many passengers at Tokyo's Haneda airport crowded into its terminals as the attack hit the year-end holiday travel season.
Offices will 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.
