The 1,018 migrants, many thought to be members of Myanmar's long-persecuted Rohingya Muslim community, landed on Langkawi late on Sunday night.
"The first capture by the police was made when a boat with the illegal immigrants was stranded at the beach in Langkawi, [and] the second capture was at Tanjung Biawak, Kuala Temonyong," said Mohd Yusof Abdullah, commander of the Langkawi marine police.
"All the illegal immigrants that have been arrested will be sent to detention centres," he added in a statement.
Police told the AP news agency that officers received a tip-off from a local fisherman that the boats were coming ashore.
Al Jazeera's Karishma Vyas, reporting from Kuala Lumpur, said that the migrants were found in "very poor condition," suffering from severe thirst and hunger.
The migrants were found a day after boats carrying about 500 members of Myanmar's long-persecuted Rohingya community washed ashore in western Indonesia.
The men, women and children arrived on two separate boats, one carrying around 430 people and the other 70, said Steve Hamilton, deputy chief of mission at the International Organisation for Migration in Jakarta, Indonesia's capital.
Last week, the UN's refugee agency said in a statement that an estimated 25,000 Rohingyas and Bangladeshis boarded people smugglers' boats in the first three months of 2015, twice as many in the same months of 2014.