The AfD party took about 21% of the vote behind the centre-left SPD’s 30%.
Angela Merkel’s CDU was backed by only about 19% of those who voted, according to the partial results.
Today’s vote was seen as a key test before German parliamentary elections in 2017.
Before it, all of Germany’s other parties ruled out forming a governing coalition with the AfD.
However, the AfD’s strong showing could weaken Angela Merkel ahead of the national elections next year.
Mecklenburg-West Pomerania, in the former East Germany, is where the chancellor’s own constituency is located.
Under Angela Merkel’s leadership, Germany has been taking in large numbers of refugees and migrants – 1.1 million in 2015 – and anti-immigrant feeling has increased.
The AfD, initially an anti-euro party, has enjoyed a rapid rise as the party of choice for voters dismayed by Angela Merkel’s policy.
However, its political power is limited and critics accuse it of engaging in xenophobic scaremongering.
The CDU has been the junior coalition partner in Mecklenburg-West Pomerania since 2006 and is likely to remain in the governing coalition. However, its 19% in the election is its worst ever result in the state, German broadcasters said.
Addressing supporters, local AfD leader Leif-Erik Holm said: “Perhaps this is the beginning of the end of Angela Merkel’s chancellorship today.”
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