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 $70.0 pm 9.9$ mJy at the wavelength of 350 $mu$m. 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 ($Delta alpha = 0.5$), 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, $ u_{rm b} = 1.6_{-1.0}^{+3.0} times 10^{12}$ Hz, the magnetic field was estimated as $Bsimeq1$-$4$ 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 $sim 100$ 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, $alpha sim 0.22$ (conservatively $<0.42$), is difficult to be attributed to the strong-shock acceleration ($alpha = 0.5$). Stochastic acceleration and magnetic reconnection are considered as a plausible alternative mechanism.
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