Maximilian Henry was the third son of Landgrave Albert II of Leuchtenberg. In 1642 he was appointed by his uncle Ferdinand of Bavaria the coadjutor of the Archbishopric of Cologne, and he took over the ruling of the dioceses he ruled. He was elected the Archbishop of Cologne, the Bishops of Liège and Hildesheim, and the Provost of Berchtesgaden after Ferdinand died. He was also elected the Bishop of Münster in 1683 although he never received papal confirmation. In 1657 he was also the Abbot of Stablo-Malmedy.