File photo: A Serbian flag is seen as the NATO Kosovo Force (KFOR) soldiers stand guard on a barricade at the border crossing Jarinje between Serbia and northern Kosovo on September 28, 2011. AFP
The latest flare-up between the two sides follows weeks of tensions after rioting in northern Kosovo saw 30 NATO peacekeepers injured in late May.
Serbia said the officers were armed with automatic weapons and in full military gear with GPS devices, maps and other equipment.
"This terrorist gang was arrested today at 12:38 pm deep in the territory of central Serbia in the area of the village of Gnjilica in the municipality of Raska," Petar Petkovic, the head of the Serbian government's office for Kosovo, told reporters.
Gnjilica is approximately six kilometres (four miles) from the border crossing with Kosovo.
A video published by Serbian police showed masked men hauling off a group of men in handcuffs.
The Kosovo government in Pristina dismissed the allegations, saying the group had been abducted.
Police in Kosovo said the group belonged to a border patrol unit and had gone missing after they reported an incursion of masked and armed men in the area.
Kosovo's Prime Minister Albin Kurti blamed Serbia for kidnapping the group, saying the move was likely "revenge" following the arrest of an alleged Serb paramilitary leader in Kosovo on Tuesday.
"The entry of Serbian forces into the territory of Kosovo is aggression and an aim for escalation and destabilisation," Kurti said in a statement posted on social media.
Kurti said the incident occurred inside of Kosovo's territory in the northern municipality of Leposavic.
"We demand the immediate release of the three kidnapped police officials," the prime minister added.
Tensions have been soaring between the arch rivals following Pristina's decision to install ethnic Albanian mayors in four Serb-majority municipalities.
The mayors were elected in polls held in April that were boycotted by ethnic Serb voters.
The episode was the latest in a long list of incidents to rock the area since Kosovo declared independence from Serbia in 2008 -- nearly a decade after NATO forces helped push Serbian forces out of the former province during a bloody war that killed around 13,000 people, most ethnic Albanians.
Belgrade, along with its key allies China and Russia, has refused to recognise Kosovo's independence, effectively preventing it from having a seat at the United Nations.
Kosovo is overwhelmingly populated by ethnic Albanians.
But in the northern stretches of the territory near the border with Serbia, ethnic Serbs remain the majority in several municipalities.
Serbia has long seen Kosovo as its spiritual and historical homeland, the scene of pivotal battles over the centuries. It continues to host some of the Serbian Orthodox Church's most revered monasteries.