The service says that it is not known where they are being held.
Relatives of correspondent Meret Khommadov say he was arrested by police in the Mary region, in southeastern Turkmenistan.
They said they have had no information about his whereabouts since then.
They also said that police had arrested a second correspondent, Jumadurdy Ovezov, in the same area.
The service says mobile telephones belonging to other Turkmen Service correspondents appear to be blocked and that it is impossible to contact them.