The two journalists are Alan Morison, the Australian editor of the Phuket-based news website Phuketwan, and Chutima Sidasathian, a Thai reporter who works for the site.
The case was brought by Naval Captain Panlob Komtonlok with the support of Admiral Polawat Sirodom, the navy's deputy commander.
Morison and Chutima are facing a possible five-year jail sentence and fine of 100,000 baht (3000 US dollars) under the Computer Crimes Act and another two years in prison for criminal defamation.
''Taking Phuketwan's journalists to court is absurd,'' said Benjamin Ismael, the head of the Reporters Without Borders Asia-Pacific desk.
''If the navy want to dispute the Reuters special report, which has just won a Pulitzer Prize, it can publicly give its version of events and demand the right of reply.
''By using the Computer Crimes Act to intimidate journalists, the navy is just making it obvious that it wants to conceal this sensitive information and deter any comments on this humanitarian scandal.
''We urge the court not to proceed with this improper complaint.''
Ismael added: ''This case highlights the urgent need for reform of the Computer Crimes Act, which is responsible for frequent violations of freedom of information by the authorities.
''It is also essential that the international media operating in Thailand should give this trial extensive coverage despite government pressure to ignore it.''
The special report by Reuters journalists Jason Szep and Andrew R.C. Marshall on Thai trafficking in Burma's refugees was awarded a Pulitzer Prize on March 14 for ''courageous'' reporting on the Rohingya and the ''predatory human-trafficking networks'' to which they often fall prey.
Phuketwan has meanwhile begun a symbolic countdown to May 3, World Press Freedom Day.
Thailand is ranked 130th out of 180 countries in the 2014 Reporters Without Borders press freedom index.
REUTERS has not responded to an email from Phuketwan seeking support for the principle of media freedom.
Phuketwan journalists face seven years' jail for republishing a Reuters paragraph that was part of the Pulitzer-winning series.
Reuters has not been charged. Nor have other organisations that republished the same paragraph.
Another journalist who asked similar questions received the following response yesterday from a Reuters spokesperson:
''Reuters' special report, which was the product of extensive reporting, is fair, balanced and contextualized. It looks broadly at the exodus of the Rohingya Muslims from Myanmar to Thailand. We wish to emphasize that Reuters' story does not single out the Thai Royal Navy, but explores the responsibility of all involved in patrolling the Thai seas and provides their perspectives. Reuters' report can be found here: http://www.reuters.com/article/2013/07/17/us-myanmar-exodus-specialreport-idUSBRE96G02520130717''
The Reuters' journalists deserve praise for their Rohingya coverage. Perhaps it's now time they advised Reuters' corporate spokespeople about the principles of media freedom.