The national carrier's homepage currently shows a photograph of a lizard in a top hat and tuxedo.
Malaysia Airlines confirmed its site was compromised but said customers' bookings and data were not affected.
The airline is still recovering from two disasters; the disappearance of MH370 and shooting down of MH17.
On Monday morning, the main page of its website was replaced by the words "404 - Plane Not Found" and "Hacked by Lizard Squad".
"404 Page not found" is the common error message displayed when a website cannot be loaded.
Initially the words "ISIS will prevail" appeared in the browser tab for the page, but that has since disappeared.
It is not clear why Malaysia Airlines has become the target of a cyber attack nor what connection the hack has to Islamic State, the militant group sometimes referred to as ISIS which has declared an Islamic caliphate in parts of Syria and Iraq.
Lizard Squad claimed on Twitter that it would release data from Malaysia Airlines, but did not specify what information it might have.'Not been hacked'
Malaysia Airlines confirmed in a statement that its "Domain Name System (DNS) has been compromised where users are re-directed to a hacker website".
It said "this temporary glitch does not affect [customer] bookings" and user data "remains secured". It added that it would take 22 hours to restore the website.
In March last year, flight MH370 disappeared from radar and is believed to have crashed 1,800km (1,100 miles) off Australia's west coast. A few months later MH17 was shot down over Ukraine, killing everyone on board.
The hacker group Lizard Squad previously claimed to have disrupted Sony and Microsoft operations, with gamers unable to log on to XBox Live and PlayStation platforms over Christmas.