We give a description of Kähler manifolds $M$ equipped with an integrable subbundle $ℱ$ of $TM$ of rank $n-1$ ($n=\dim M$) under the assumption that the line bundle $\mathrm{D}é\mathrm{t}ℱ$ is numerically trivial. This is a sort of foliated version of Bogomolov’s theorem concerning Kähler manifolds with trivial canonical class.