The men will be held in custody until their first court hearing on charges that carry up to three years in jail or a fine for the import and export of "restricted or banned goods" without obtaining a license.
"We have opened a case against all four -- two foreigners and two Burmese. They will be held on remand until November 10," deputy police colonel Kyaw Moe told AFP.
The pair was working with well-known Myanmar journalist Aung Naing Soe and a local driver Hla Tin.
The incident comes as tensions surge between Myanmar and Turkey, which has led criticism of the Southeast Asian nation for its treatment of the persecuted Rohingya Muslim minority.
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Turkey's President Recep Tayyip Erdogan has accused Myanmar of incubating "Buddhist terror" and carrying out a genocide against the Muslim group.
More than 600,000 Rohingya have fled Myanmar's Rakhine state since late August, running from burning villages they say were set alight by soldiers and Buddhist mobs.
Many have been charged with defamation or arrested for reporting on armed rebel groups.
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