He is the son of Titus Shadrack Sishosonke Dlungwane and Amalia MaZuma Dlungwane, who are both deceased. He was born at Impendle in a place called Enzinga.
He attended his primary education at Clairvaux Mission School up to 1960. He then did his Std 5 at Mariathal Mission School in 1961. In 1962, he was sentto Aloisianum where he spent where he spent two years (1962-1963). After which he moved to St. Mary's Seminary from 1964-1968. Mlungisi's application for major seminary studies was accepted by Bishop Alphonse Streit, who at the time decided to send his seminarians to St. Augustine's Seminary in Lesotho.
He was ordained as a priest by Bishop Martin Schmid on the 4th of July 1976. As a young priest, he was locum tenens at Assisi Mission for three months and at Mophela Mission for five months. In April 1977 he was appointed assistant priest at Mariatrost Mission under Fr. Walter Tauer CMM for a year and three months. About mid year of 1978 he was transferred to KwaNdengezi, where a new parish community called St. Kizito was being established. He was also serving at St. Xavier in Dassenhoek until June 1980, where after he was sent to St. Francis College as a rector.
However, greater need for personnel arose at St. Mary's Minor Seminary in Ixobho, Mlungisi was then transferred to the Minor Seminary in 1983 by Bishop Paul Themba Mngoma. Then, the SACBC requested him to be released to join the formation staff at St. John Vianney Seminary.
For his further studies in theology he went to the University of Saint Paul in Ottawa, Canada, where he obtained Masters and Licentiate degrees in theology. Then, from 1993 up to 1995 he served as a vice-rector and lecturer at St John Vianney Seminary. In 1996 he returned to the university to complete his doctoral research in Biblical Theology. In 1997 he was awarded conjointly a Doctorate in Theology and PhD by the University of St. Paul and the University of Ottawa, respectively.
In 1998, Fr Mlungisi was appointed rector of St. John Vianney National Seminary. To a lesser extent, he also taught the Synoptic Gospels. In the year 2000, Pope John Paul II appointed him auxilliary bishop of Mariannhill, to help Bishop PT Mngoma who was not well. On the 7th of February 2005, Pope John Paul II accepted Bishop Mngoma's request to retire. At the same time Bishop MP Dlungwane was appointed administrator of Mariannhill. On the 3rd of June 2006 Pope Benedict XVI appointed him as the Bishop of Mariannhill.