He received his episcopal consecration on 7 August from Cardinal Juan Landázuri Ricketts, Archbishop of Lima.

On 6 February 1996, Pope John Paul named him head of the Military Ordinariate of Peru where he took office on 7 March 1998.

[1] Pope John Paul named him a member of the Pontifical Commission for Latin America on 5 July 2004.

[5][b] Cabrejas submitted his resignation as archbishop to Pope Francis in 2023 as he reached the mandatory retirement age of 75.

On 11 February 2025, his resignation was accepted by the Vatican amid criticism over his failure to stop abuses by the Catholic organization Sodalitium Christianae Vitae when he was president of the Peruvian Episcopal Conference.