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.