The 34 men, 14 women and three children - including a two-month-old girl, are thought to have boarded the fishing boat on December 28 as they tried to sneak out of Malaysia to return to Indonesia's Sumatra island, The Star reported.
But the vessel suffered engine problems and drifted until maritime personnel spotted it on Thursday off northern Perak state, the report added.
The immigrants were weak from hunger and shaken by bad weather that rocked the boat, Razak Johan - an official with the Malaysian Maritime Enforcement Agency - told the paper.
Razak and other officials could not immediately be reached for comments.
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Around two million Indonesians and others from poorer regional countries are estimated to work illegally in Malaysian plantation, construction, factory and other jobs.
They often use rickety boats to sneak in and out of the Southeast Asian country, and accidents are common.
Seven Indonesians died and 33 others went missing when their boat sank in rough seas on their way home to celebrate Eid al-Fitr, the end of the Muslim fasting month, in August.
Four were found and rescued and the other 29 are presumed dead.