According to a police spokeswoman, the gunman opened fire in the building with an automatic rifle, shouting "Allahu Akbar" - Arabic for "God is great".
Zvornik is in the Bosnian Serb part of the country, near the Serbian border.
Thousands of Bosnian Muslims in Zvornik were killed or expelled by Serbian forces during the 1992-95 war.
"This is the worst terrorism attack that could happen in the Serb Republic," Dragan Lukac, the region's interior minister, told local television.
Mr Lukac said the security level had been raised in the region.
The two officers wounded in the attack did not have life-threatening injuries, doctors said.
The Bosnian Serb government is expected to hold an emergency session on Monday night.
The imam of the mosque in Zvornik, Mustafa Muharemovic, has condemned the attack, the Associated Press news agency reports.
The country, officially called Bosnia-Herzegovina, is made up of two semi-autonomous regions - the Bosniak-Croat Federation and the Bosnian Serb Republic. Each has its own president, government, parliament, police and other bodies.
A police station in the Bosniak-Croat Federation was targeted by bombers in 2010. The attack killed one officer and wounded five others.
In 2011, a gunman attacked the US embassy in the capital Sarajevo, injuring one policeman.
A gunman has attacked a police station in the Bosnian town of Zvornik, killing an officer and injuring two others before being shot dead, officials say.