Using an isospin-dependent transport model, we study isospin effects on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei at intermediate energies. We find that these correlation functions are sensitive to the density dependence of nuclear symmetry energy, but not to the incompressibility of symmetric nuclear matter and the medium dependence of nucleonnucleon cross sections. This sensitivity is mainly due to effects of nuclear symmetry energy on the emission times of neutrons and protons as well as their relative emission sequence. We also study the variations of the symmetry energy effects on nucleon-nucleon correlations with respect to the impact parameter, incident energy, and mass number of heavy ion collisions.