More than 30 million voters are eligible to cast ballots to pick nearly 47,000 municipal and regional representatives and about 2,500 mayors.
The second round will be held on November 30.
According to opinion polls, the Civic Platform, in power since 2007, will have a comfortable edge over its main rival, the conservative Law and Justice Party.
The Civic Platform is tipped to win about 32 percent of the vote against 27 percent for the main opposition Law and Justice Party.
Poland is obliged to join the single currency bloc as part of its 2004 European Union entry deal but has dragged its feet on the move, which would require it to amend its constitution.