The COVID-19 pandemic has led to a surge in medical waste generation, posing hazards to both the environment and global health. The impacts of the COVID-19 pandemic’s medical waste hazard may persist long after the pandemic itself subsides. Improper disposal of medical waste can contaminate environment, posing risks to ecosystems and public health. Discarded medical rubber gloves, for example, can become a source of infection, improper disposal of these gloves can escalate the spread of infectious diseases and increase the risk of transmission of the virus to the general public. This study proposes an innovative and sustainable method to reinforce cement mortar by adding recycled glove rubber as an additive to cement mortar to increase its resistance to impact loads. This study conducted uniaxial compression tests, separating hopkinson pressure bar (SHPB) experiments and SEM observations to evaluate the quasi-static compressive strength and dynamic stress of recycled rubber fiber mortar (RRFM) with varying recycled rubber fiber (RRF) contents (0, 1%, 2%, 3%). Strain curves, dynamic increase factor (DIF), energy absorption rules, failure modes, and microstructure of RRFM mixtures. The experimental results demonstrate that with the addition of RRF, the dynamic stress-strain curve flattens and the peak strain gradually increases. The RRFM sample shows stronger toughness. In comparison to regular cement mortar (NM), RRFM has a higher DIF and specific absorbed energy, a faster increase in dynamic compressive strength, and the ability to absorb more energy per unit volume. Under the same impact load, RRFM has fewer and smaller cracks than NM. Scanning electron microscopy (SEM) testing also observed that RRF formed a strong connection pattern with the cement mortar matrix.