The SPD, junior partners in Merkel's right-left national government, lost their ruling majority in the northwestern state of Lower Saxony when a coalition deputy jumped ship.
"I consider it essential that the state parliament now dissolve and new elections take place as soon as possible in Lower Saxony," said Stephan Weil, premier of the state, which is home to auto giant Volkswagen.
Weil said he has no plans to resign.
"I will face up to the will of voters at any time, but I will not bow to intrigue," he said, in a veiled accusation that the rebel deputy, Elke Twesten of the Greens party, was part of a wider plot to torpedo his government.
Twesten had earlier announced her intention to join the conservative Christian Democrats (CDU) following a "long process of alienation" with her party.
The SPD-Greens coalition had governed the state since 2013 with a one-seat majority.
Lower Saxony was due in January to hold its state election, which is now likely this November. A poll this week saw the SPD trailing the CDU in the state by a 14-point margin.
The ruction in the normally tranquil summer holiday period marks a major setback for the Social Democrats.
On the national level, the SPD is trailing 18 points behind Merkel's CDU ahead of the September 24th election, according to a poll published on Wednesday by independent opinion research firm Forsa.
Voters' view of Merkel as a safe pair of hands in a turbulent world and the rude health of the German economy are major challenges for SPD candidate Martin Schulz, a former European Parliament president.