We propose that the Hubble tension can be understood as a dynamical consequence of octonionic non-associativity. A physically relevant realization requires a genuinely nontrivial associator sector, which necessarily involves multiple octonionic fields. We therefore construct the minimal triplet model with three octonion-valued scalar fields and a covariant associator norm contribution ∥A(Ψ1,Ψ2,Ψ3)∥2 in the action. From this action we derive the Einstein equations, the coupled octonionic matter equations, and the homogeneous FLRW reduction. In the resulting effectivecosmology, the associator sector can be suppressed in the early universe while remaining nonzero at late times, thereby generating a redshift-dependent deformation of the expansion history. This produces a framework in which early-universe observables remain close to the standard backgroundwhile late-time observables can infer a larger effective Hubble scale. We also formulate a directly testable phenomenological parametrization suitable for confrontation with Pantheon+ and DESI DR2. Current data do not yet establish a unique global best fit for the octonionic parameters, but they do show that a late-time, redshift-dependent departure from strict ΛCDM remains phenomenologically viable and is qualitatively aligned with the kind of deformation generated by the octonionic associator sector.