The exciton properties of Si/Si1-x Ge (x) cylindrical quantum wires (QWRs) are calculated using the variational method and taking into account the existence of an interface layer between the materials. We consider two possibilities for the conduction band lineup, type-I and type-II. Our numerical results show that an interfacial fluctuation of 15 angstrom in a Si (0.85) Ge (0.15) (Si0.70Ge0.30) type-I (type-II) wire of 50 angstrom wire radius leads to an exciton energy blue shift of the order of 10 (10) meV.