Polarization maps of the Vela C molecular cloud were obtained at 250, 350, and 500 μm during the 2012 flight of the balloon-borne telescope BLASTPol. These measurements are used in conjunction with 850 μm data from Planck to study the submillimeter spectrum of the polarization fraction for this cloud. The spectrum is relatively flat and does not exhibit a pronounced minimum at λ ∼ 350 μm as suggested by previous measurements of other molecular clouds. The shape of the spectrum does not depend strongly on the radiative environment of the dust, as quantified by the column density or the dust temperature obtained from Herschel data. The polarization ratios observed in Vela C are consistent with a model of a porous clumpy molecular cloud being uniformly heated by the interstellar radiation field.