Among them are several imams, including the head of Pristina's Grand Mosque, Shefqet Krasniqi, local reports say.
Some 200 Kosovo Albanians have gone to fight in Syria and several have died.
IS is thought to have attracted hundreds of European recruits in its campaign to set up a "caliphate" in broad swathes of Syria and Iraq.
Kosovo police did not name those arrested, publishing only their initials, but said the operation had been carried out following threats and due to the importance of national security.
Many of those held were from Pristina, Prizren or the flashpoint town of Mitrovica