We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information.The fundamental properties of the quantifier such as convexity,superadditivity,monotonicity,and conservation relations are revealed.The quantifier is illustrated by a variety of typical examples,and applications to the quantification of nonclassical correlations are discussed.Various extensions are indicated.