Suu Kyi steered her National League for Democracy (NLD) into power earlier this year after championing a decades-long struggle against military rule.
Her administration has vowed to expand freedoms in the fledgling democracy but limits on expression remain - as does a culture of charging critics with defamation.
The latest case saw two men charged for allegedly going on an obscenity-laced rant against the Nobel Laureate after a heavy evening drinking session in a village not far from the capital Naypyidaw.
"An NLD member sent a complaint letter to the police and sued two people for abusing the state counsellor," he told AFP.
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"We know these two people but we have not arrested them yet," he added.
According to local news site the Democratic Voice of Burma, the two men called Suu Kyi a "hag" who deserved to be murdered.
Suu Kyi is adored by many in Myanmar and her party trounced historic polls in November, the first free election in decades.
Despite soaring hopes her administration would nurture a new era of free expression, several people have been prosecuted for defamation since her party took over in late March.
In July a local official in central Magway region was charged with defamation for referring to Suu Kyi with a slur on Facebook.