We present high-angular (~0.4") resolution mid-infrared (MIR) polarimetric observations in the 8.7 and 11.6 micron filters of Cygnus A using CanariCam on the 10.4-m Gran Telescopio CANARIAS. A highly polarized nucleus is observed with a degree of polarization of 11+/-3% and 12+/-3% and position angle of polarization of 27+/-8 degrees and 35+/-8 degrees in a 0.38" (~380 pc) aperture for each filter. The observed rising of the polarized flux density with increasing wavelength is consistent with synchrotron radiation from the pc-scale jet close to the core of Cygnus A. Based on our polarization model, the synchrotron emission from the pc-scale jet is estimated to be 14% and 17% of the total flux density in the 8.7 and 11.6 micron filters, respectively. A blackbody component with a characteristic temperature of 220 K accounts for >75% of the observed MIR total flux density. The blackbody emission arises from a combination of (1) dust emission in the torus; and (2) diffuse dust emission around the nuclear region, but the contributions of the two components cannot be well constrained in these observations.