Halide perovskites have been recently shown to exhibit strong nonlinear optical properties such as two-photon absorption, second harmonic generation, etc. In this work, the nondegenerate two-photon absorption, i.e., when the energies of two photons absorbed are not the same, of methylammonium lead bromide single crystal is studied. It is found that the nondegenerate two-photon absorption is much stronger than the degenerate two-photon absorption. For the photon pair ℏω = 2.96 eV, ℏω = 0.73 eV, the nondegenerate two-photon absorption coefficient reaches 51.3 cm GW, which is around 6 times that of degenerate two-photon absorption. Taking advantage of the strong nondegenerate two-photon absorption, a nonlinear infrared pulse photodetector based on the combination of a methylammonium lead bromide single crystal and a silicon photodiode is developed. The infrared femtosecond laser pulses at 1700 nm can be well measured with a resolution on the order of 1 nJ and responsivity of 68 V W. These findings provide novel insight for the understanding of nondegenerate nonlinear optical properties in halide perovskites and may open a new avenue for the development of high-sensitivity infrared photon detection.