The investment in the 800 square metre restaurant added up to 2.5 million marka ($1.7 million/1.3 million euro), the municipal authorities said in a statement.
The Serb Republic is one of the two autonomous entities making up Bosnia and Herzegovina. The other one is the Muslim-Croat Federation.
McDonald's already has restaurants in the towns of Sarajevo and Mostar, both located in the Federation.
(1 euro = 1.95583 Bosnian marka)