This would be in contrast to Mrs Merkel's previous position, in which she has linked the party leadership role to the chancellorship - meaning that she would only remain chancellor if she was party leader.
"With these latest results, it has simply become untenable that Merkel continues to lead the CDU", said Mujtaba Rahman, managing director at Eurasia Group, a consultancy.
Die Welt reporter Robin Alexander said the path could now be clear for Merkel's chosen heir, CDU general secretary Annegret Kramp-Karrenbauer, to take the reins if no other credible candidate emerges by December.
"The CDU should make way for a new start in a government or a new election in Germany", he told German television channel NTV.
She said she would stay on as German Chancellor until her term expires in 2021.
"She was genuinely sad and not at all bitter and asked that the discussion about her succession be conducted in a kind manner", the source said, adding that Merkel's words were greeted with a standing ovation. The hard-right, xenophobic Alternative for Germany (Afd) came in just under 13 per cent, triple the vote it received four years ago.
When Hesse last elected its state legislature in 2013 - on the same day that Mrs Merkel was triumphantly elected to a third term as chancellor - they won 38.3% and 30.7%, respectively. Merkel had been widely expected to run for re-election, although plummeting party poll numbers and disappointing election results suggested that she could face a challenge.
Age: 45Role: State premier of Schleswig-Holstein Guenther emerged from relative obscurity previous year to take Germany's northernmost state in a valuable electoral boost to Merkel.
Merkel's predecessor, Gerhard Schroeder, stepped down as leader of his centre-left Social Democrats in 2004 as his government struggled, but remained chancellor until he narrowly lost an election 18 months later.
But with Germany, and Europe, becoming ever-more polarised, challengers are likely to push for the party to tack hard to the right. On October 14, the Christian Social Union, or CSU - the Bavarian sister party to the CDU - lost its majority in the Bavarian state parliament. But she said today that she had changed her mind over the northern summer as it became clear that "we can not continue with business as usual".
Merkel's announcement set off a flurry of speculation in the German media over who would succeed her.
The Social Democrats also saw huge losses in the elections.
Merkel, 64, a trained scientist raised behind the Iron Curtain, long held the support of German voters as a guarantor of stability and prosperity, notably during the global financial crisis and eurozone turmoil.