Conventional concrete significantly affects the environment due to high CO2 emission into the atmosphere during the production process. In order to improve concrete performance and arrest the incidence of global warming, the use of additive materials for cement replacement has been promoted worldwide. This study was designed to investigate the mechanical properties of high-performance fiber-reinforced concrete (HFRC) produced using rice husk ash (RHA) and hybrid fiber (HF) in accordance with the densified mixture design algorithm (DMDA) mix design method. Samples were produced using RHA as a direct replacement for cement at 10%, 20%, and 30%. HF, comprising steel and polypropylene fibers, was added (by volume) to the 20% RHA group mixture to improve the HFRC sample properties. Based on the experimental results, higher RHA contents had a generally negative effect on the fresh properties of the HFRC mixtures. Compressive strength values ranged from 53 to 72 MPa with various RHA and HF content. RHA replacement levels up to 20% had an insignificant effect on the strength development and dynamic modulus of the HFRC samples. However, the addition of HF improved splitting tensile strength, flexural strength, and dynamic modulus remarkably at all curing ages. Furthermore, the 91-day drying shrinkage was in the ranges of 0.032%–0.039% and 0.023%–0.034% using different RHA and HF levels, respectively. Increasing both RHA and HF contents significantly reduced drying shrinkage in the samples. Multivariable regression was also performed, clarifying that all tested results were consistent and had good correlations. The results of this study also provide a potentially effective use for abundantly available industrial waste products such as fly ash (FA) and RHA to promote the production of greener and more sustainable concrete.