Cross sections for the collision-induced reactions between protonated ammonia cluster ions, NH4+(NH3)(n-1) (n=3-9), with ND3 were measured at a collision energy ranging from 0.02 to 1.4 eV in the center-of-mass frame with an extremely narrow energy distribution of 0.02 eV. Two types of reaction, incorporation and dissociation, were observed at the same collision energy. The incorporation cross section increased drastically with a decrease in the collision energy, especially in the collision energy region below about 0.2 eV. The incorporation cross section at a collision energy of about 0.02 eV was larger than twice the geometrical reaction cross section. It is suggested that the increase of the incorporation cross section corresponds to the increase of the collision cross section between the cluster ion and the neutral molecule at the low collision energies used in this study because of the presence of the electrostatic attractive force. The reaction probability for incorporation also increased with a decrease of the collision energy. The collision energy dependence of the probability was studied in more detail for NH4+(NH3)(4) of which the incorporation cross section can be precisely evaluated, due to its simple spherical structure, by trajectory simulations. This increase was interpreted to be due to the recoil energy of the molecule, which was dependent upon the collision energy and the internal energy of the cluster ion. The size dependence of the incorporation cross section indicated that the incorporation cross section of the pentamer ion NH4+(NH3)(4) was at a minimum in the cluster size region (n=3-9) at very low collision energies. The size dependence of the incorporation cross section is discussed in relationship to the structure of the cluster ions.