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.
Mrs Merkel has reportedly told CDU party leaders that she will step aside from the leadership election bid after the centre-right party and the centre-left SPD both took a hit in ballots in Hesse state at the weekend.
However, she said that she would like to remain chancellor, local media report.
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