Sri Lanka's navy has arrested 32 people suspected of being Rohingya refugees and their Indian traffickers off the country's northern coast.
Chaminda Walakuluge, a navy spokesman, said a coastguard patrol observed the boat entering Sri Lankan waters on Sunday.
The 30 passengers from Myanmar included 16 children, among them a baby just 15 days old and a four-month-old child.
The two Indians were suspected of being their traffickers.
Walakuluge said the suspects had been handed over to police for further inquiries.
Tens of thousands of Rohingya Muslims have fled Myanmar's Rakhine state since the military began a security operation last October in response to what it says was an attack by Rohingya armed men on border posts, in which nine police officers were killed.
Last month Aung San Suu Kyi, Myanmar's leader, denied reports saying security forces carried out ethnic cleansing of the country's Rohingya Muslims, despite the United Nations and human rights groups saying a crackdown by the army may amount to crimes against humanity.
Aung San Suu Kyi, a Nobel peace laureate whose international star as a rights defender is waning over the treatment of the Rohingya, has not condemned the crackdown and has not spoken out in defence of the persecuted minority.
Instead, she has called for space to handle the issue in a country where the more than one million Rohingya are not recognised as an ethnic minority and widely vilified as "illegal" immigrants from Bangladesh - even though many have lived in Buddhist-majority Myanmar for generations.
A UN report released in February said the army's campaign targeting the Rohingya involved mass killings, gang rapes and the burning down of villages, likely amounting to crimes against humanity and ethnic cleansing.
In neighbouring Bangladesh, where more than 75,000 Rohingya have fled to escape the crackdown, people have recounted grisly accounts of horrendous army abuse, including soldiers allegedly executing an eight-month-old baby while his mother was gang-raped by five security officers.
"What kind of hatred could make a man stab a baby crying out for his mother's milk," Zeid Raad al-Hussein, the UN rights chief, said in a statement at the time.
"What kind of 'clearance operation' is this? What national security goals could possibly be served by this?"
Source: News agencies