The men were arrested over the weekend in Yangon and fined USD 800 each yesterday after pleading guilty to an offence that carries up to two years in prison.
Myanmar's government does not recognise the term Rohingya and insists the minority group does not face official persecution.
"They admitted and confessed very fast. So the court charged them one million kyat (around USD 800) each," Khin Maung Let, chief police officer at Pazundaung township, told AFP.
Khin Maung Let said police were initially alerted to the calendar via Facebook with officers subsequently raiding a printing press on the outskirts of Yangon.
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"The calendar contained words and photos saying the Rohingya are an ethnic minority of Myanmar. That is against the law and such activity threatens the law and order of the country," he added.
A sixth suspect is on the run, he said.
Myanmar's Printing and Publishing Law bans publishing materials that could damage national security and law and order.
The UN and other rights groups have condemned their treatment in western Rakhine state where they face restrictions over employment and travel with many living in bleak displacement camps.
Hundreds of thousands of Rohingya were unable to vote in this month's landmark elections after their citizenship was cancelled.
The government says the majority are illegal immigrants from Bangladesh, despite the fact that many have lived in the country for generations.