The footage, first screened on Wednesday at the trial of former Yugoslav president Slobodan Milosevic at the UN tribunal in The Hague, showed six teenage boys with their hands bound being unloaded from a truck and shot in the back.
The soldiers are believed to be from the notorious “Scorpions” paramilitary unit, linked to the Serbian interior ministry.
Around 8,000 Muslim men and boys were executed when Bosnian Serb forces backed by the Milosevic regime overran the UN-protected enclave of Srebrenica in eastern Bosnia in 1995.
Serbian Prime Minister Vojislav Kostunica announced the arrests on Thursday after meeting with UN prosecutor Carla Del Ponte in Belgrade.
“Since yesterday several suspects implicated in this crime have been arrested. It was important to react immediately on the basis of this video which was shocking and terrible for all of us,” Mr Kostunica said.
He didn’t identify the suspects or reveal how many had been arrested.
Serbian state television reported that at least ten men, including the alleged commander of Scorpions, were arrested.
Rasim Ljajic, the country’s top official in charge of cooperation with the UN tribunal, confirmed “more than eight people, suspected of execution of Srebrenica’s Muslims” had been arrested.
Considered the worst atrocity in Europe since World War II, the Srebrenica massacre has led to genocide charges against suspects including Milosevic, former Bosnian Serb president Radovan Karadzic and his military commander, Ratko Mladic.
The video, excerpts of which were shown on Serbian television, came as a deep shock to the former Yugoslav republic where many people deny the massacre took place.
Ms Del Ponte praised the arrests by Serbia authorities but urged them to follow up by arresting Mladic and Karadzic who still remain at large 10 years after being indicted.
Mr Kostunica dismisses Ms Del Ponte’s claims that Mladic is being protected by rogue elements of the Serbian military.
His political rival, President Boris Tadic, said the gruesome video was clear evidence of the “monstrous crimes” committed by Serb forces during Bosnia’s 1992-1995 war.
Serbia-Montenegro Foreign Minister Vuk Draskovic said “bringing to justice all those indicted for war crimes is our primary national obligation”.