Nonlinear nanophotonics, as an emerging field in nanophotonics, eagerly calls for experimental techniques for probing and analyzing near-field nonlinear optical signals with subwavelength resolution. Here, we report an aperture-type scanning near-field optical microscopic method for probing near-field nonlinear optical processes. As a demonstration, near-field third-harmonic generation from an anapole dark-mode state generated by a silicon nanodisk is probed and imaged. The measured results agree well with the simulations, with a spatial resolution down to $0.14{\lambda _0}$ and a sensitivity of 0.1 nW. This method provides a powerful tool for characterizing nonlinear light-matter interactions at the nanoscale, which can help, for example, to unveil crystal properties involving subwavelength defects or dislocations.