Dodik says that the signing of the law leads to the reintroduction of "constitutional jurisdiction" in Republika Srpska.
Bosnia and Herzegovina's Foreign Minister Elmedin Konaković condemns Dodik's decision and says that it "follows the pattern of a coup", according to the Bosnian media company FTV.
Since the Dayton Agreement, which put an end to the civil war in 1992-1995, which claimed nearly 100,000 lives, Bosnia and Herzegovina has been divided into two largely autonomous parts.
They are the Federation, where mainly Bosniaks and Bosnian Croats live, and the Serbian Republic (Republika Srpska), where the majority are Bosnian Serbs.
Dodik was sentenced to one year in prison and banned from holding office for six years for refusing to comply with decisions made by the UN High Representative in Bosnia and Herzegovina, German Christian Schmidt, who is tasked with overseeing the Dayton Agreement.
The Republika Srpska parliament then adopted the law in response to the verdict.
Dodik, 65, has the right to appeal the verdict. He describes the trial as political, aimed at "eliminating him from the political arena".
