One of the open questions following the discovery of GW170817 is whether neutron star (NS) mergers are the only astrophysical sites capable of producing r-process elements. Simulations have shown that 0.01-0.1 M(circle dot )of r-process material could be generated in the outflows originating from the accretion disk surrounding the rapidly rotating black hole that forms as a remnant to both NS mergers and collapsing massive stars associated with long-duration gamma-ray bursts (collapsars). The hallmark signature of r-process nucleosynthesis in the binary NS merger GW170817 was its long-lasting near-infrared (NIR) emission, thus motivating a systematic photometric study of the light curves of broad-lined stripped-envelope (Ic-BL) supernovae (SNe) associated with collapsars. We present the first systematic study of 25 SNe Ic-BL-including 18 observed with the Zwicky Transient Facility and 7 from the literature-in the optical/NIR bands to determine what quantity of r-process material, if any, is synthesized in these explosions. Using semi-analytic models designed to account for r-process production in SNe Ic-BL, we perform light curve fitting to derive constraints on the r-process mass for these SNe. We also perform independent light curve fits to models without the r-process. We find that the r-process-free models are a better fit to the light curves of the objects in our sample. Thus, we find no compelling evidence of r-process enrichment in any of our objects. Further high-cadence infrared photometric studies and nebular spectroscopic analysis would be sensitive to smaller quantities of r-process ejecta mass or indicate whether all collapsars are completely devoid of r-process nucleosynthesis.