A flare kernel associated with a C4 class flare was observed in a spectral window including the He i triplet 10830 Å and Si i 10827 Å with a spectropolarimeter on the Domeless Solar Telescope at Hida Observatory on 2015 August 9. The observed Stokes profiles of the He i triplet in the flare kernel in its post-maximum phase are well reproduced through inversions considering the Zeeman and the Paschen–Back effects with a three-slab model of the flare kernel, in which two slabs which have upward and downward velocities produce emissions and one slab produces an absorption. The magnetic field strength inferred from the emission components of the He i line is 1400 G, which is significantly stronger than 690 G that is observed at the same location in the same line 6.5 hr before the flare. In addition, the photospheric magnetic field vector derived from the Si i10827 Å is similar to that of the flare kernel. To explain this result, we suggest that the emission in the He i triplet during the flare is produced in the deep layer, around which bombardment of non-thermal electrons leads to the formation of a coronal temperature plasma. Assuming a hydrogen column density at the location where the He i emissions are formed, and a power-law index of non-thermal electron energy distribution, we derived the low-energy cutoff of the non-thermal electron as 20–30 keV, which is consistent with that inferred from hard X-ray data obtained by RHESSI.