Several researchers devoted considerable efforts to partially replace natural aggregates in concrete with recycled materials such as recycled tire rubber. However, this often led to a significant reduction in the compressive strength of rubberized concrete due to the weaker interfacial transition zone between the cementitious matrix and rubber particles and the softness of rubber granules. Thereafter, significant research has explored the effects of supplementary cementitious materials such as zeolite, fly ash, silica fume, and slag used as partial replacement for cement on rubberized concrete properties. In this study, systematic experimental work was carried out to assess the mechanical properties of palm oil fuel ash (POFA)-based concrete incorporating tire rubber aggregates (TRAs) using the response surface methodology (RSM). Based on the findings, reasonable compressive, flexure, and tensile strengths were recorded or up to 10% replacement of sand with recycled tire fibre and fine TRAs. In particular, the reduction in compressive, tensile, and flexural strengths of POFA concrete incorporating fibre rubber decreased by 16.3%, 9.8%, and 10.1% at 365 days compared to normal concrete without POFA and rubber. It can be concluded that utilization of a combination of POFA and fine or fibre rubber could act as a beneficial strategy to solve the weakness of current rubberized concrete’s strength as well as to tackle the environmental issues of the enormous stockpiles of waste tires worldwide.