The move came as rights groups raise concerns about efforts by the new pro-democracy government to amend draconian laws on demonstrations.
Dozens of activists and students marched through Yangon on Saturday in a rare gesture of religious solidarity in the diverse nation, where rising Buddhist nationalism has stoked anti-Muslim sentiment and sporadic bouts of bloodshed in recent years.
Police said they decided to take action against five rally leaders - believed to be three women and two men of several faiths - because the campaigners had deviated from the agreed protest route.
"We have started legal action against five protest leaders under Section 19 of the Peaceful Assembly Act," police Lieutenant Major Win Tin from Kyauktada township told AFP.
Suu Kyi's party is stacked with former dissidents who served prison time for their opposition to Myanmar's military governments during decades of repressive rule.
They are now in government following a landslide November election victory.
Since taking the helm the administration has freed scores of activists and political prisoners and signalled its determination to repeal oppressive laws.
"You don't need these punishments in your draft. If you remove these three or four things then it's pretty good and you won't be condemning another generation of peaceful protesters for breaking a flawed law," said David Mathieson of Human Rights Watch.
He said the revised law would still give "carte blanche to abusive local officials" to prosecute activists and urged a rethink.
The proposed draft would mean protesters must still give local police 48 hours' notice of the place and time of any rally, as well as details of planned speeches and slogans.
Parliament is due to debate the law in the coming days.
