Online news site indeksonline said police officers were attacked by about 60 people during the raid in northern Mitrovica late Wednesday and three were slightly injured.
The Red Cross of Serbia, a branch of the international Red Cross, also works in Kosovo to support the country's ethnic Serb minority.
Some people in the organization are suspected of trying to register people as living in Kosovo, which would be illegal since "the population census is held by Kosovo's competent institutions," police said.
There was no immediate comment from the Serbian Red Cross.
No arrests were made, but Kosovo police have launched criminal cases against suspects who allegedly attacked their officers.
Serbian Foreign Minister Ivica Dacic reacted angrily to news of the raid, which he said was part of "the continuation of pressure against (Kosovo) Serbs." The ministry will provide legal assistance to support Serbs in Kosovo, he said.
"Look what we came to when the Red Cross is considered an enemy," Dacic told Serbia's state TV.
Tensions between Kosovo and Serbia have escalated since December.
Kosovo suspended European Union-sponsored talks with Serbia after the new prime minister, Ramush Haradinaj, was arrested in France on a warrant from Serbia in January. A French court refused to extradite him.
Kosovo declared independence from Serbia in 2008, but Serbia has not recognized it as a separate country and seeks to maintain influence in northern Kosovo, where most of the Serb minority lives.