The clashes also forced more than 650,000 people, mostly Muslim inhabitants in northern Rakhine, to flee to the neighbouring Bangladesh to escape violence.
The two are due to appear in court on Wednesday.
Ko Wa Lone, one of two detained Reuters reporters, displays his handcuffs before being taken back to Insein Prison after the pair's court hearing on Wednesday in Yangon.
"If any person for any objective prejudicial to the safety or interest of the State obtains, collects, records or publishes or communicates to any other person any secret official code or password, or any sketch, plan, model, article or note or other document or information which is calculated to be or might be or is meant to be, directly or indirectly, useful to an enemy", they could be punished with time in prison, that particular section of the law states.
The Ministry of Information had previously cited police as saying they were "arrested for possessing important and secret government documents related to Rakhine State and security forces".
A request for bail has been submitted to the court, which the judge will review at the next hearing on January 23, the lawyer said. The court took it under consideration and will decide at the next hearing on January 23, he said.
The reporters were detained on December 12 after they had been invited to meet police officers over dinner. It has given no further information on the police arrested.
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About 50 reporters gathered in front of the court to protest the arrest. Several had the message "journalism is not a crime" or "release the arrested journalists now" on their T-shirts.
The two journalists arrived and left court in handcuffs.
"According to the section, the two journalists can not get bail".
Reuters said it was "extremely disappointed" that the authorities were seeking to prosecute.
It is a case that highlights growing concerns about press freedom in the country.
Numerous journalists have been imprisoned after reporting on abuses taking place in Myanmar's ethnic frontier lands, where the military has been fighting various ethnic guerrilla groups for decades.
Wa Lone said, "They arrested us to prevent us from finding the truth".
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A government spokesman was not available for comment on Clinton's Twitter post. "Their actions are wrong and unfair". "The media freedom that is so critical to rule of law and a strong democracy requires that journalists be able to do their jobs". "These two men should be released immediately and unconditionally".
Reuters journalists Wa Lone and Kyaw Soe Oo after their arrest in an image published by the Myanmar's Information Ministry. Authorities have largely banned media from the conflict zone.
"We therefore call on your government to provide the necessary legal protection for these two journalists, to ensure the full respect of their fundamental rights and to release them immediately".
Rights and media groups have criticised Myanmar's civilian government for continuing to use colonial-era laws to threaten and imprison journalists. In 2014, he joined the English-language Myanmar Times, covering the 2015 election that swept Nobel peace prize laureate Aung San Suu Kyi to power.
Wa Lone joined Reuters in 2016 and made his mark with reports on sensitive subjects.
Both the government and the army have denied the accusations.
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