Rohingya migrants trying to travel south by boat have been rare since Thai authorities clamped down on regional trafficking networks in 2015, leaving thousands of migrants abandoned in open waters or jungle camps.
Almost 700,000 Rohingya have been driven out of Rakhine state and are living in crowded refugee camps in Bangladesh since the Burmese military began a "clearance operation" in August.
Al Jazeera's Wayne Hay reports from Bangkok.
A Bangladeshi official also said Monday that a Burmese government official would visit the Rohingya refugee camps near the Bangladeshi-Burma border next week, making them the first high-ranking official to do so. The boats also leave from Bangladesh, and their passengers are not always all Rohingya.
The UNHCR said it was in touch with Malaysian maritime authorities and was ready to provide any necessary assistance to the refugees when they arrived.
A displaced Rohingya man who lives near Sittwe confirmed Lewa's account, saying there had been only three boats that he knew of that had left Sittwe since December, one going to Bangladesh and the second seemingly having disappeared.
The navy chief said that all of the boat's passengers were safe but exhausted and hungry, and were given food and water.
The UN had called it as "a textbook ethnic cleansing".
Suu Kyi made only a passing reference to the crisis in Rakhine state, where her government faces mounting worldwide condemnation for a military operation against Rohingya Muslims.
Muslim-majority Malaysia, which has not signed the UN Refugee Convention and treats refugees as illegal migrants, is already home to more than 100,000 Rohingya refugees.
Zulkifili said the refugees would be handed over to immigration authorities for humanitarian reasons, an indirect indication that they will be allowed to stay rather than sent back to sea.
He said some of the tribal groups have family in Rakhine and these relatives are being used to woo the Bangladeshi tribals.
Rohingya in the refugee camps and the worldwide community have called for guarantees of a safe return and establishment of protected areas in Rakhine before repatriation begins.