The contests in Thuringia and Saxony come just over a week after three people were killed in a suspected Islamist attack, which has fuelled a bitter debate over immigration in Germany.
Opinion polls have the anti-immigration Alternative for Germany (AfD) ahead in Thuringia and a close second in Saxony, while also predicting a strong showing for the upstart far-left BSW.
The two parties have found a receptive audience in the eastern states for their criticism of the government in Berlin and of military aid to Ukraine.
An election victory for the AfD would be a landmark in Germany's post-war history and represent a rebuke for Scholz ahead of national elections in 2025.
In both states, Scholz's Social Democrats are polling at around six percent, while their coalition partners, the Greens and the liberal FDP, lag even further behind.
But even if the AfD does come out on top in the elections, it is unlikely to come to power because other parties have ruled out working with the far right to form a government.
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Voting stations close at 6:00 pm (1600 GMT), with the first exit polls expected shortly after.
Far-right rise
Casting her vote early in Erfurt, the capital of Thuringia, Sandra Pagel said she was "really afraid" of a victory of the AfD.
"I'm very nervous to see what happens today... because I think there's a very high risk that the AfD will win and that scares me. For my grandchildren and also for me," said the 46-year-old sterilisation processing facility manager.
Created in 2013 as an anti-euro group before morphing into an anti-immigration party, the AfD has capitalised on the fractious three-way coalition in Berlin to rise in opinion polls.
In June's EU Parliament elections, the party scored a record 15.9 percent overall and did especially well in eastern Germany, where it emerged as the biggest force.
In a post on social media platform X on Sunday, AfD co-leader Alice Weidel urged voters to choose the AfD to "not only change the future in Saxony and Thuringia, but also bring about a political turnaround throughout Germany".
Saxony is the most populous of the former East German states and has been a conservative stronghold since reunification.
Thuringia meanwhile is more rural and the only state currently led by the far-left Die Linke, a successor of East Germany's ruling communist party.
A third former East German state, Brandenburg, is also due to hold an election later in September, where polls have the AfD ahead on around 24 percent.
The picture in each state is slightly different but "in any case, it is clear that the AfD will unite a very strong number of votes behind it", Marianne Kneuer, a professor of politics at the Dresden University of Technology (TU Dresden), told AFP.
READ ALSO: How similar are Germany's AfD and BSW parties?
The AfD has found stronger support in the east where more voters "identify with its nationalist and authoritarian positions" and many are dissatisfied with the mainstream parties, Kneuer said.
At the party's last campaign meeting on Saturday in Erfurt, the capital of Thuringia, Thorsten Haentzsche, a 52-year-old voter, said he was "dreaming of an absolute majority" for the AfD.
"But we are realistic. A score of at least 33 percent would be great because it would give us a blocking minority in the (regional) parliament," he said.
New challenger
The run-up to the votes in Saxony and Thuringia has been dominated by an outcry over immigration stirred up by the deadly stabbing in the western city of Solingen.
The alleged attacker, a 26-year-old Syrian man with suspected links to the Islamic State group, was slated for deportation but evaded attempts by authorities to remove him.
The government has sought to respond to the alarm by announcing stricter knife controls and rules for migrants in Germany illegally.
At a commemoration for the victims of the attack on Sunday, President Frank-Walter Steinmeier insisted that "the majority of people in our country want to live together peacefully in a society that is guided by humanity and not by hatred".
"Fanatical Islamists want to destroy what we love: our open society, our way of life, our community, our freedom," he said.
Alongside the AfD, new party BSW has also found a receptive audience in the eastern states for its criticism of the government in Berlin and of military aid to Ukraine.
Like the AfD, Wagenknecht and her party have made hay with a dovish stance towards Russia and calls for a radical crackdown on immigration.
BSW scored an immediate success in June's European elections, hauling in around six percent of the German vote, and is polling a strong third in Saxony and Thuringia.
Other parties' refusal to work with the AfD leaves BSW as potentially the kingmaker in Thuringia and Saxony, despite serious policy disagreements with potential partners, especially on Ukraine.
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