Her decision comes after her party suffered heavy losses in regional elections that threatened the stability of the governing coalition.
Mrs Merkel has been chair of the CDU since 2000, becoming one of its longest-serving chairpersons.
She has led Germany as chancellor since 2005 - and wants to stay in that post.
However, news of Mrs Merkel decision could spark a race within the CDU to find her successor as chancellor.
The position is usually determined in Germany's federal elections, the next of which are provisionally scheduled for 2021.
What has Angela Merkel said?
Mrs Merkel has reportedly told leaders of her Christian Democratic Union (CDU) party that she will step aside from the leadership election bid after the centre-right party and the centre-left Social Democrats (SPD) both took a hit in ballots in Hesse state at the weekend.
However, she said that she would like to remain in the post of Germany's chancellor until 2021, local media report.
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.
Angela Merkel's leadership woes
Germany's marriage of convenience
The BBC's Jenny Hill, in Berlin, says the latest setback comes amid a terrible year for the chancellor where her coalition government has lurched unhappily from crisis to crisis.
However, the battle scarred Mrs Merkel is a political survivor - our correspondent adds - and renouncing the leadership of her party might just silence critics within her own ranks, for now.
Why has Merkel lost support?
Mrs Merkel, the country's first female chancellor, rose to power on the image of a prudent and pragmatic leader.
It was, however, her open-door refugee policy that sparked public concern and helped fuel parties like the far-right Alternative for Germany (AfD).
Angela Merkel's quiet power
The Greens have also grown in national suppor
Mrs Merkel's migration policy has exposed the fragility of her divided coalition government - and even within her own political group.
Sexual assaults by migrants in Cologne and Islamist attacks in Germany all dented the chancellor's popularity.
Mrs Merkel has stopped short of admitting making a mistake, but has said "if I could, I would turn back the clock many years" to prepare Germany better for the influx of arrivals.
Who will replace her as chairperson?
Among the potential candidates are ambitious Health Minister Jens Spahn; the Prime Minister of North Rhine-Westphalia, Armin Laschet; and the woman seen as Mrs Merkel's anointed heir, Annegret Kramp-Karrenbauer.
Following news of Mrs Merkel's decision on Monday, former CDU parliamentary group leader Friedrich Merz indicated that he wanted to join the race for party leadership, Reuters news agency reports
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