Two-photon fluorescence spectroscopy of negatively charged nitrogen-vacancy [(N-V)(-)] centers in type Ib diamond single crystals have been studied with a picosecond (7.5 ps) mode-locked Nd:YVO4 laser operating at 1064 nm. The (N-V)(-) centers were produced by radiation damage of diamond using a 3 MeV proton beam, followed by thermal annealing at 800 degrees C. Prior to the irradiation treatment, infrared spectroscopy of the C-N vibrational modes at 1344 cm(-1) suggested a nitrogen content of 109 +/- 10 ppm. Irradiation and annealing of the specimen led to the emergence of a new absorption band peaking at similar to 560 nm. From a measurement of the integrated absorption intensity of the sharp zero-phonon line (637 nm) at liquid nitrogen temperature, we determined a (N-V)- density of (4.5 +/- 1.1) x 10(18) centers/cm(3) (or 25 +/- 6 ppm) for the substrate irradiated at a dose of 1 x 10(16) H+/cm(2). Such a high defect density allowed us to observe two-photon excited fluorescence and measure the corresponding fluorescence decay time. No significant difference in the spectral feature and fluorescence lifetime was observed between one-photon and two-photon excitations. Assuming that the fluorescence quantum yields are the same for both processes, a two-photon absorption cross section of sigma(TPA) = (0.45 +/- 0.23) x 10(-50) Cm-4 center dot s/photon at 1064 nm was determined for the (N-V)center based on its one-photon absorption cross section of sigma(OPA) = (3.1 +/- 0.8) x 10(-17) cm(2) at 532 nm. The material is highly photostable and shows no sign of photobleaching even under continuous two-photon excitation at a peak power density of 3 GW/cm(2) for 5 min.