Press Information Department has published photos of the meeting held on Monday morning (local time) at the UN Headquarters in New York, where the global leaders have gathered for the 71st UN General Assembly.
Hasina and Myanmar Foreign Minister Suu Kyi, who have played key role in establishing democracy in their countries, were having a lively discussion in the photos. Their fathers were independence heroes.
But what they discussed was not immediately disclosed.
The two countries have a dispute over Rohingya refugees. Over 500,000 Muslim Rohingyas from Myanmar have been in Bangladesh's refugee camps for decades.
Hasina reached New York on Sunday after visiting Canada. She is scheduled to address the UNGA on Wednesday.
Before meeting Suu Kyi, the prime minister addressed the plenary session of the UNGA, which focused on migrants and refugees.
Later in the day, Hasina will co-chair a round table on global migration that will seek to focus on human rights for migrants in the context of 2030 agenda for sustainable development.
On the same day, she will attend a meeting on refugee issues organised by US President Barack Obama that will be followed by a reception.
On Sep 22, the prime minister is scheduled to meet Swiss President Johann Schneider-Ammann and later join the inaugural session of the Global Deal Initiative organised by the Swedish prime minister.
Later that afternoon, Hasina will address the UN General Assembly before attending a reception hosted by Bangladeshi expatriates in the evening.
She will also address a press conference in the Bangladesh mission in New York on that day.
On the sidelines of the General Assembly, Hasina is scheduled to meet the heads of several other states, the Commonwealth secretary general, the World Economic Forum executive chairman and the World Bank president.
The prime minister will leave New York for Virginia on Sep 22.
She will take an Emirates flight from Washington DC on Sep 25 and reach Dhaka the next day.