Malaysia's Communications and Multimedia Commission said that 51 websites in the .gov.my domain were attacked beginning late Wednesday, and that 41 of the sites suffered various levels of disruption.
The MCMC, the country's Internet and telecommunications regulator, did not however provide information on the nature of the attacks, or the people behind it, describing them only as "unknown hackers".
However, it made references to some of the websites recovering quickly, suggesting that these sites faced a DDoS or distributed denial-of-service attack rather than a hack.
DDoS attacks can make a website inaccessible to users by swamping the website with traffic from hundreds or thousands of computers.
Such attacks are a known tactic of Anonymous, a hacker group that had threatened to attack Malaysia.
The MCMC had noticed a reduction in the levels of attack by 4 a.m. local time Thursday, it said. The attacks had little effect on Malaysian users, and most of the websites have already recovered, it said.
"We do not expect the overall recovery to these websites to take long," it said.
"The public is advised to report any information they may have regarding the identity of these hackers as the act to disrupt network services is a serious offence," it said.
Anonymous has used various online forums to threaten Malaysia with an attack in protest against the government's decision to block 10 websites that reportedly allowed the download of pirated content. Earlier this week, Anonymous invited people to join Operation Malaysia, targeting a government website from 7.30 p.m. GMT on Wednesday (3.30 a.m. Thursday, local time).