Backing for Merkel's coalition partner, the centre-left Social Democrats (SPD), also plummeted, falling from 31 per cent to 20 per cent - a low not seen in 72 years.
After the vote, SPD leader Andrea Nahles called the result "unacceptable" and left open the possibility that her party could bolt from Merkel's already precarious coalition - a move that would collapse the Government. "We will have to see if the SPD is still able to govern," she said.
As the country's two traditionally dominant centrist parties flailed in Hesse, forces on either flank surged: The far-right Alternative for Germany (AfD) and the progressive Greens. The latter was vying with the SPD for second place after its best result in the state's history.
The outcome was an almost exact replay of results in Bavaria two weeks ago, when the CDU's sister party, the Christian Social Union (CSU), was humiliated in a state where it has long governed without rivals. After that vote, Merkel allies blamed the CSU's rightward lurch on immigration for its poor results.
But today's vote suggests the CDU's image has also taken a strong hit during a year when the nation's politics have been overshadowed by a sustained feud within Merkel's Government.
The CDU has governed Hesse for nearly 20 years, and the party campaigned on an enviable record in the state of ultra-low unemployment, high wages and minimal crime.
But analysts said that voters treated the election as a referendum on the national Government, and their reviews were poor.
"The message was very clear: Don't quarrel. Get together. Be the strong Germany that Europe needs," said Sigrid Rossteutscher, an analyst at Frankfurt's Goethe University.
Still, the CDU seemed to have avoided a worst-case scenario in Hesse: The potential humiliation of losing control of the state, as left-leaning parties appeared to have fallen short of the backing needed to form a government on their own.
That means the CDU will almost certainly remain in charge, with the Greens and the centrist Free Democrats as likely coalition partners.
A fall from power in Hesse had been seen as possible prelude to a much more consequential shake-up for the party. The CDU hosts its annual conference in December, and Merkel, who has governed Germany for the past 13 years, will be seeking re-election as party chairwoman.
Had the party relinquished control in Hesse, some analysts saw her as vulnerable to an intraparty challenge. Although the CDU has remained relatively united behind its leader in public, discontent has been building as the party's fortunes have sunk.
The results in Bavaria and Hesse mirror political trends nationwide. The CDU won a third of the vote in last September's German election - an historically poor performance for a party that has dominated the country's post-war politics. But current polls show the CDU not even winning a quarter of the national vote.
The SPD has seen a similarly steep drop nationally, with Germany's oldest political party falling from second place to fourth, behind the Greens and the AfD.
Rossteutscher said the SPD will be reluctant to bring down Merkel's Government because party leaders know that if they do, and early elections are called, the SPD "would be the biggest loser".
The AfD claimed nearly 13 per cent of the vote - almost exactly the same percentage that it won in last year's national elections - and a place in Hesse's Parliament for the first time.
Just five years after the party's founding as a protest against euro zone bailouts, the anti-immigrant AfD now controls seats in all 16 of Germany's state parliaments, in addition to the national Bundestag and the European parliament.
"The election was a success on all fronts," said the AfD's leader in Hesse, Jörg Meuthen.
But the night's biggest winner was the Greens.
The party nearly doubled its support from 2013, picking off defectors from both the CDU and the SPD. The result, coupled with a similarly impressive second-place finish in Bavaria, proved that there's new vitality on the left of German politics.
"Before this election, we thought a new political movement was possible only from the far right," said party co-leader Robert Habeck. " Now we see that a democratic, optimistic, trend is possible, too."
