Determination of the explosion type of supernova remnants (SNRs) can be challenging, as SNRs are hundreds to thousands of years old and supernovae (SNe) are classified based on spectral properties days after explosion. Previous studies of thermal X-ray emission from Milky Way and Large Magellanic Cloud (LMC) SNRs have shown that Type Ia and core-collapse (CC) SNRs have statistically different symmetries, and thus these sources can be typed based on their X-ray morphologies. In this paper, we extend the same technique, a multipole expansion technique using power ratios, to infrared (IR) images of SNRs to test whether they can be typed using the symmetry of their warm dust emission as well. We analyzed archival Spitzer Space Telescope Multiband Imaging Photometer (MIPS) 24 micron observations of the previously used X-ray sample, and we find that the two classes of SNRs separate according to their IR morphologies. The Type Ia SNRs are statistically more circular and mirror symmetric than the CC SNRs, likely due to the different circumstellar environments and explosion geometries of the progenitors. Broadly, our work indicates that the IR emission retains information of the explosive origins of the SNR and offers a new method to type SNRs based on IR morphology. ; Comment: 6 pages, 4 figures; accepted by ApJL