Olivier Ndjimbi-Tshiende, 66, told parishioners of his decision during a church service on Sunday in Zorneding, a small town near Munich in Bavaria.
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A statement on the parish website (in German) said: “We are shocked and saddened by these [death] threats.” He began preaching in the town in 2012.
Tensions had arisen between him and two local conservative CSU politicians.
Fr Ndjimbi-Tshiende criticised language used by local CSU leader Sylvia Boher in October. She had spoken of an “invasion” by Eritrean “refugees from military service”.
The surge in asylum seekers entering the EU includes many Eritreans fleeing military service, to avoid years spent in deplorable conditions for little or no pay.
After Fr Ndjimbi-Tshiende’s intervention a CSU friend of Ms Boher, Johann Haindl, lashed out at the priest with a racist insult.
Both CSU politicians were heavily criticised over the affair and resigned from their party posts.
The Christian Social Union (CSU), based in Bavaria, is politically allied with Chancellor Angela Merkel’s Christian Democrats (CDU).
Police are now investigating a suspected crime of racial incitement and abuse targeting Fr Ndjimbi-Tshiende.
Germany is struggling to accommodate record numbers of non-EU migrants – 1.1 million asylum seekers were registered last year.
German media say the priest, born in the Democratic Republic of Congo, had received five death threats.
An online petition (in German) has been launched urging him to stay in Zorneding. But the Catholic Church Archbishopric in Munich plans to transfer him to a new post on 1 April.
The local broadcaster BR says that in 2014 a school project to help 35 child refugees in Zorneding triggered a barrage of xenophobic emails.