The elections are seen as a test of Kosovo's readiness to organise democratic elections on its own, having been run by the UN until it seceded from Serbia in 2008.
"This Sunday should prove to the world that Kosovo is a stable country that produces peace and stability in the region," Fatmir Sejdiu, the Kosovan president, said, calling for a big turnout for the polls.
Kosovo's leaders and international officials have called for peaceful elections following renewed tensions between rival ethnic Albanian parties that threatened to overshadow the vote.
In the latest such incident, Nato peacekeepers were called on Saturday to remove a hand grenade found outside an opposition party's offices in a town in the north.
Several ethnic Albanian political parties, including the junior partner in the governing coalition, have warned of potential fraud, raising doubts about the aftermath of the vote.
The polling stations are due to open at 7am (0600 GMT) and close twelve hours later, with the first unofficial results expected by midnight.
A runoff will be organised on December 13 in municipalities where candidates fail to win more than 50 per cent of vote in the first round.
So far, 63 countries recognise Kosovo as a state, including the US and most countries in the EU.
But Serbia has vowed to block further recognition and has Russia's support.
About 120,000 Serbs live in Kosovo. They rejected the independence declaration and have kept strong links with authorities in Belgrade, receiving financial and political support from the Serbian government.
The UN took over control of Kosovo from Serbia in 1999, until 2008.