We obtain a general formula for the low frequency absorption cross section of spherically symmetric black holes in d dimensions including leading string-theoretical alpha'-corrections. We show that for nonextremal black holes this covariant formula must be given in terms of the horizon area and temperature, while for extremal black holes it is simply given in terms of the horizon area.Classically, this cross section equals four times the black hole entropy; by applying these formulas for the cross section to known solutions, we discuss when such relation with the entropy is preserved including the alpha'-corrections.