The latest polls showed the far-right Alternative for Germany neck-and-neck with the Social Democrats, which has governed the state continuously since 1990.
ADVERTISEMENTVoting began on Sunday morning in Brandenburg state, three weeks after a far-right party made gains in two other states in eastern Germany.
Around 2.1 million people are registered to vote for a new state parliament in Brandenburg, the state that surrounds Berlin, the capital of Germany.
Sunday's election is being watched closely for signs about the country's political direction.
The Social Democrats, the largest party in Chancellor Olaf Scholz's three-way coalition government, are hoping to maintain control of their stronghold in the face of rising support for parties on the extreme right and left.
If the Social Democrats lose in Brandenburg, where Scholz himself has his constituency, it would be seen as a bad sign for him a year before federal elections are due to be held.
The far-right Alternative for Germany won the most votes and also did well in Saxony on elections held on Sept. 1, generating concerns in Germany and abroad about growing support for the extreme right in the largest European Union country.
The far-right party has gained support amid a growing backlash to large-scale migration to Germany over the past decade and several recent extremist attacks.
Even if it wins in Brandenburg, it is unlikely to govern because other parties have refused to work with it.