[6] In 1993, he was appointed Coadjutor Bishop of Mỹ Tho and promoted to Archbishop of Hồ Chí Minh City in 1998.

He officiated at a mass in La Vang in 1998 for the 200th anniversary of the apparition of the Virgin Mary, the largest Vietnamese Catholic event up to that time.

On 7 March 2013, Mẫn was the last cardinal to arrive to attend the 2013 papal conclave to select the successor to Pope Benedict XVI.

On 28 September 2013, Pope Francis appointed Bishop Paul Bùi Văn Đọc, previously (since 1999) serving as Bishop of the Roman Catholic Diocese of Mỹ Tho, Vietnam (one of the Archdiocese of Hồ Chí Minh City's suffragan dioceses), as Coadjutor Archbishop of the Archdiocese.

[9] On 22 March 2014, Pope Francis accepted the resignation of Cardinal Mẫn due to age limit.