The vessel went down in choppy waters off Malaysia's western coast near the coastal town of Sabak Bernam in central Selangor state, Mohamad Aliyas Hamdan, the local head of the Malaysian Maritime Enforcement Agency, told AFP.
"Local fishermen have rescued 13 people and have found 13 bodies," he said.
Based on the size of the boat, it could have been carrying about 70 people but local fishermen said there could have been up to 100 migrants on board, he added.
The authorities have yet to interview the victims to confirm their nationality. The bodies will be taken to taken to a public hospital Teluk Intan in neighbouring Perak state.
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"We are not sure if the migrants were attempting to land in Malaysia or trying to leave Malaysia illegally," Aliyas said, describing the sinking as the worst boat tragedy so far this year.
Malaysia, Southeast Asia's third largest economy, has been a magnet for Indonesians in search of jobs.
But maritime accidents are frequent as thousands attempt the perilous sea crossing, despite the risks, to seek low-paying jobs -- typically shunned by Malaysians -- on plantations, construction sites and in factories.
Indonesians often add to the risk by choosing to cross the Malacca Strait in darkness to avoid detection.