The men were initially taken into custody over the weekend in Yangon and fined USD 800 each on Monday after pleading guilty to a publishing law offence.
But they have now been rearrested and jailed on separate charges of inciting alarm or panic, a charge that carries up to two years jail.
"We arrested five persons yesterday under the warrant by the court. They were sent to Insein prison," Khin Maung Latt, police chief of Pazundaung township, told AFP, referring to the city's notorious junta era prison.
Myanmar's government does not recognise the term Rohingya, arguing that the Muslim minority are illegal immigrants from Bangladesh, despite the fact that many have lived in the country for generations.
Use of the term has become both sensitive and dangerous in recent years as Myanmar undergoes a surge of Buddhist nationalism and anti-Muslim sentiment.
Local media reported that the arrests of the men came after hardline Buddhist nationalist group Ma Ba Tha complained about the calendar. Parmaukkha, a monk and prominent Ma Ba Tha member, said the organisation had not placed pressure on police to rearrest the men.
"Regarding the calender, we cannot accept it at all because we do not have Rohingya in our Myanmar history," he said.
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