In a statement posted on its site on Monday, the company said it had blocked external access to applications as soon as it detected the attack, to prevent the malware from spreading.
But CMA CGM did not say when it had detected the attack.
According to a report on Lloyd's List, the group's Chinese offices were hit by cyber criminals using the Ragnar Locker ransomware.
"Our teams are fully mobilised and access to our information systems is gradually resuming," the company said in its statement.
"The CMA CGM network remains available to the Group's customers for all booking and operation requests.
"An investigation is underway, conducted by our internal experts and by independent experts.
"A new communication will be issued at the end of the day."
CMA CGM, which has been in business for 42 years, is a family business group founder by entrepreneur Jacques Saadé.
The current chairman and chief executive is Rodolphe Saadé. The group has 110,000 employees in 160 countries.
Of itself, the company says: "From one ship, four employees and a single maritime link between Beirut, Latakia, Livorno and Marseille, the company has grown to become one of the world’s leading container shipping and logistics groups with 502 vessels calling at 420 ports in 160 countries, 750 warehouses and 110,000 dedicated employees working out of 755 offices worldwide."
iTWire has contacted CMA CGM for comment.
Thanks to Bleeping Computer for a link to the Lloyd's List story.