Far-Infrared (FIR) photometry from the Photodetector Array Camera and Spectrometer on the Herschel Space Observatory is presented for 313 nearby, hard X-ray selected galaxies from the 58 month Swift Burst Alert Telescope (BAT) Active Galactic Nuclei catalog. The present data do not distinguish between the FIR luminosity distributions at 70 and 160{mu}m for Seyfert 1 and Seyfert 2 galaxies. This result suggests that if the FIR emission is from the nuclear obscuring material surrounding the accretion disk, then it emits isotropically, independent of orientation. Alternatively, a significant fraction of the 70 and 160{mu}m luminosity could be from star formation, independent of active galactic nucleus (AGN) type. Using a non-parametric test for partial correlation with censored data, we find a statistically significant correlation between the AGN intrinsic power (in the 14-195keV band) and the FIR emission at 70 and 160{mu}m for Seyfert 1 galaxies. We find no correlation between the 14-195keV and FIR luminosities in Seyfert 2 galaxies. The observed correlations suggest two possible scenarios: (1) if we assume that the FIR luminosity is a good tracer of star formation, then there is a connection between star formation and the AGN at sub-kiloparsec scales, or (2) dust heated by the AGN has a statistically significant contribution to the FIR emission. Using a Spearman rank-order analysis, the 14-195keV luminosities for the Seyfert 1 and 2 galaxies are weakly statistically correlated with the F_70_/F_160_ratios.