Angela Merkel's conservative Christian Democrats (CDU) have suffered a humiliating defeat in a key German regional election – a blow that will make governing all the more difficult for her already shaky coalition.

The CDU lost control of Hamburg to the opposition SPD party, which won 48.3% of the vote – enough to win an absolute majority with 62 of the 121 seats in the city-state's parliament.

The CDU took just 21.9% – its worst result in Germany's second city since the second world war.

The dramatic plunge in support for Merkel's party, which polled 42.6% of the vote at the last election in Hamburg, in 2008, can be attributed to voter dissatisfaction with the chancellor's handling of the euro crisis as well as problems within her own party at home – and particularly in Hamburg.

Merkel herself stayed silent but public statements made by her closest aides suggest she believes the defeat was not her fault. Seven minutes after the result last night, her chief of staff, Eckart von Klaeden, went on TV to point out that the Hamburgers were voting "80% on local issues" rather than national ones.

But commentators insist the result will trouble the chancellor deeply. A headline in the Süddeutsche Zeitung labelled it: "An earthquake that will shake Berlin." In the story, the CDU general secretary Hermann Gröhe admitted it had been a "serious defeat" and that his party had suffered "great losses".

Merkel will be hoping the result will not be repeated elsewhere. This year has been described as "super election year" in Germany, with a six more states due to go to the polls.

The next big test for her will come at the end of March in the south-western region of Baden-Württemberg, where the CDU is in danger of losing power because of fierce arguments over plans for a multibillion-euro station in Stuttgart.

The Hamburg result marks a welcome upturn for the SPD, which has struggled nationally since the former SPD chancellor Gerhard Schröder dissolved his coalition government with the Greens in 2005.

Although Merkel is likely to remain chancellor until the next national election in 2013, the shift of power in Hamburg, where she had campaigned hard, will make it even more difficult for her federal coalition to pass laws.

This is because, in selecting the makeup of their regional parliament, the Bürgerschaft, Hamburgers also choose who their state sends to the powerful Bundesrat, Germany's upper house of parliament.

The Bundesrat has to approve about half the legislation that passes through the Bundestag lower house.

In May, the coalition lost its slim majority in the Bundesrat after elections in North Rhine-Westphalia, Germany's most populous state.

Merkel's party, which has been recovering nationally from a plunge in popularity last year, is facing fresh setbacks.

The popular defence minister, Karl-Theodor zu Guttenberg, has been embroiled in a plagiarism scandal over his PhD thesis. The Bundesbank chief, Axel Weber, who was seen as a key contender for the top job at the European Central Bank, said he would quit the German central bank – a decision many have interpreted as a blow to Merkel.

Hamburg, long a leftwing bastion, was ruled by the SPD for 44 years before it lost power to Merkel's CDU 10 years ago.

In the port city on Sunday, the Green party increased its vote from 9.6% in 2008 to around 11.2% this time. Despite bettering their result, the Greens were disappointed that the scale of the CDU defeat meant the SPD did not need them to form a coalition.

The centrist FDP, which rules on a national level with the CDU, also upped its vote slightly from 4.8% to 6.6%, while the Left party's share of the vote remained static at 6.4%.

The CDU plunged in Hamburg polls after its leader, Christoph Ahlhaus, a lawyer, took over from the popular CDU mayor, Ole von Beust, who abruptly quit in July. A CDU coalition with the Greens failed in November, triggering the elections.

Nationally, Merkel's conservatives are at about 36%. The SPD (22%) and their preferred partners, the Greens (20%), are just ahead of the ruling coalition of Merkel's conservatives and their FDP partners (5%) combined.

There had been concerns in Hamburg that a new and complicated voting system which allowed voters to tick up to 20 boxes would bamboozle the electorate.

The local authorities were so worried about confusion that they set up a special voting helpline to offer voters advice on how to correctly fill in their forms. 57% of the 1.3 million Hamburgers eligible to vote did so – a slight drop on turnout in 2008.