The organization said about 1,000 demonstrators in Yangon rallied for peace in the restive state of Kachin.
Human Rights Watch said 13 protesters face charges for allegedly violating laws on public assembly.
Demonstrators told the rights organization they went ahead with a protest despite the government's concern about public safety. A law on public assembly allows peaceful dissent, though Human Rights Watch said restrictions remain in place for protests that are viewed as offensive or threatening.
Myanmar's government received international praise for political reforms, though ethnic disputes and human rights remain issues.
Phil Robertson, deputy director for Asian programs at Human Rights Watch, said Myanmar's "reformist label" is at risk given its alleged intolerance for dissent.
"The charges against the peace march organizers should be dropped immediately," he said in a statement from New York.
Myanmar kicked off reforms with general elections in 2010. Nobel Peace Prize laureate Aung San Suu Kyi, a former longtime prisoner, serves in the country's legislative assembly.
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