The authors extend to bundles over quaternionic Kähler manifolds the by now classical notion of self-duality over 4-dimensional spaces. This condition has a twistor interpretation in terms of twistors over quaternionic Kähler manifolds, a notion of the second author and L. Bérard Bergery. Interesting examples of self-dual connections over projective quaternionic spaces are constructed using an extension of the monad construction of Atiyah-Hitchin-Manin-Drinfeld.