The ministry said in a statement that three Georgian journalists, Tea Shariya, Tariel Sokhadze and Teimuraz Eliava, were shooting a film about architectural monuments when detained in Abkhazia on March 2.
"All three citizens were brutally beaten up and taken to a detention ward in Sukhumi," the statement said. "They need medical attention, but the Abkhazian separatist administration does not allow representatives from the UN military observers mission and a doctor to see them."
The Georgian ministry asked the United Nations, the Organization for Security and Cooperation in Europe (OSCE) and others to take measures to secure the journalists' release.
Abkhazia's foreign minister, Sergei Shamba, said earlier that the detained were members of a Georgian religious non-governmental organization and did not have a permission to cross the border. He said all journalists and NGO members from Georgia going to Abkhazia had to notify his ministry about their visits.
Abkhazia proclaimed independence from Georgia after bloody conflicts in the early 1990s following the collapse of the Soviet Union, but has failed to gain international recognition. Tbilisi has repeatedly accused Moscow of siding with separatists in the breakaway province, which has soured relations between the two countries.