Dodik, president of Bosnia's autonomous Serb Republic, was indicted in 2023 for signing laws that suspended rulings by the constitutional court and by international peace envoy Christian Schmidt.
Dodik has rejected the indictment as politically motivated.
Under criminal law, Bosnians can pay a fine instead of facing jail time if the sentence is no more than one year.
The court also banned Dodik from engaging in politics for six years over his separatist actions.
The verdict could trigger a crisis in Bosnia, which suffered a bloody ethnic conflict the 1990s and has since been split into two autonomous regions: the Serb-dominated Republika Srpska and the Federation shared by Croats and Bosniaks, linked via a central government.
The two regions were given wide autonomy but kept some joint institutions, including the army, top judiciary and tax administration.
Bosnia also has a rotating three-member presidency made up of Bosniak, Serb and Croat members.
Dodik was in the Bosnian Serb administrative capital Banja Luka, where thousands gathered on Wednesday in his support.
"They say I am guilty but now people here will say why I am not guilty," Dodik told the crowd shortly after the verdict was announced.
"There is no reason to worry. I have learned to deal with tougher situations. It is important that you are here."
Dodik suggested the Bosnian Serb parliament could ban the work of the state prosecutor, the state court and the intelligence agency in the Serb Republic area of Bosnia after the court ruling.
with AP
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