A far-infrared counterpart to the west hot spot of the radio galaxy Pictor A is discovered with the Spectral and Photometric Imaging REceiver (SPIRE) onboard Herschel. The color-corrected flux density of the source is measured as 70.0 ± 9.9 mJy at the wavelength of 350 µm. A close investigation into its radio-to-optical spectrum indicates that the mid-infrared excess over the radio synchrotron component, detected with WISE and Spitzer, significantly contributes to the far-infrared band. Thanks to the SPIRE data, it is revealed that the spectrum of the excess is described by a broken power-law model subjected to a high-energy cutoff. By applying the radiative cooling break under continuous energy injection (∆α = 0.5), the broken power-law model supports an idea that the excess originates in 10-pc scale substructures within the hot spot. From the break frequency, ν b = 1.6 +3.0 −1.0 × 10 12 Hz, the magnetic field was estimated as B ≃ 1-4 mG. This is higher than the minimum-energy magnetic field of the substructures by a factor of 3-10. Even if the origin of the excess is larger than ∼ 100 pc, the magnetic field stronger than the minimum-energy field is confirmed. It is proposed that regions with a magnetic field locally boosted via plasma turbulence are observed as the substructures. The derived energy index below the break, α ∼ 0.22 (conservatively < 0.42), is difficult to be attributed to the strong-shock acceleration (α = 0.5). Stochastic acceleration and magnetic reconnection are considered as a plausible alternative mechanism.