Summary: The present paper treats transversal holomorphic maps in the foliation context. We show that such a map for Kähler foliations is a transversal harmonic map with the minimum energy in its foliated homotopy class. Our results extend by A. Lichnerowicz [Sympos. Math., Roma 3, Probl. Evolut. Sist. solare, Nov. 1968 e Geometria, Febb. 1969, 341–402 (1970; Zbl 0193.50101)], S. Ianus and A. M. Pastore [Proceedings of the conference, Brest, France, 1997. Boca Raton, FL: Chapman & Hall/CRC. Chapman Hall/CRC Res. Notes Math. 413, 67–73 (2000; Zbl 0947.53034)], C. Gherghe and K. Kenmotsu [Differ. Geom. Appl. 21, No. 1, 55–63 (2004; Zbl 1067.53051)] and by D. Fetcu [Balkan J. Geom. Appl. 9, No. 2, 13–24 (2004; Zbl 1075.53024)].