We present near-infrared (NIR) and optical observations of the Type Ic supernova (SN Ic) SN 2021krf obtained between days 13 and 259 at several ground-based telescopes. The NIR spectrum at day 68 exhibits a rising K-band continuum flux density longward of ~2.0{mu}m, and a late-time optical spectrum at day 259 shows strong [OI]6300 and 6364{AA} emission-line asymmetry, both indicating the presence of dust, likely formed in the SN ejecta. We estimate a carbon-grain dust mass of ~2x10^-5^M_{sun}_ and a dust temperature of ~900-1200K associated with this rising continuum and suggest the dust has formed in SN ejecta. Utilizing the one-dimensional multigroup radiation-hydrodynamics code STELLA, we present two degenerate progenitor solutions for SN 2021krf, characterized by C-O star masses of 3.93 and 5.74M_{sun}_, but with the same best-fit ^56^Ni mass of 0.11M_{sun}_ for early times (0-70 days). At late times (70-300 days), optical light curves of SN 2021krf decline substantially more slowly than those expected from ^56^Co radioactive decay. Lack of H and He lines in the late-time SN spectrum suggests the absence of significant interaction of the ejecta with the circumstellar medium. We reproduce the entire bolometric light curve with a combination of radioactive decay and an additional powering source in the form of a central engine of a millisecond pulsar with a magnetic field smaller than that of a typical magnetar.