"Meeting a valued friend. PM @narendramodi with the State Councillor Aung San Suu Kyi," External Affairs Ministry spokesperson Raveesh Kumar tweeted.
The prime minister's visit to Myanmar comes amid a spike in ethnic violence with Rohingya Muslims in the Rakhine state.
He is expected to raise the issue of the exodus of the ethnic Rohingyas into neighbouring countries.
The Indian government is also concerned about Rohingya immigrants in the country, and has been considering to deport them. Around 40,000 Rohingyas are said to be staying illegally in India.
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Modi arrived here on the second leg of his two-nation trip during which he travelled to southeastern Chinese city Xiamen where he attended the annual BRICS summit and held talks with Chinese President Xi Jinping, Russian President Vladimir Putin and other world leaders.
This is Modi's first bilateral visit to Myanmar. He had visited the country in 2014 to attend the ASEAN-India Summit.
The Myanmarese president and Suu Kyi had visited India last year.