Recently, Chen established a general sharp inequality for warped products in real space forms. As applications, he obtained obstructions to minimal isometric immersions of warped products into real space forms. Afterwards, Matsumoto and one of the present authors proved the Sasakian version of this inequality. In the present paper, we obtain sharp estimates for the warping function in terms of the mean curvature for warped products isometrically immersed in Kenmotsu space forms. Some applications are derived.