[citation needed] Feige was ordained a priest on 1 July 1978 for the Diocese of Magdeburg and worked in Salzwedel.

[citation needed] Since 2004, Feige has served as one of two co-chairmen of the Saint Irenaeus Joint Orthodox-Catholic Working Group, an ecumenical group of Catholic and Eastern Orthodox theologians—clerics and lay people—which promotes unity and investigates the differences between these Christian traditions.

[1] Feige is a member of the Dicastery for Promoting Christian Unity and a chairman of the Ecumenical Commission of the German Bishops' Conference.

[2][3] When asked about the potential ordination of women in January 2019, Feige said that the question remained open while recognizing that such a path is unlikely.

[4] In January 2020, Feige, the then-head of the German bishops' commission on ecumenism, voiced skepticism about a recent proposal by German theologians to give Protestants the ability to receive Communion in Catholic churches.