We develop a mathematically explicit and physically transparent derivation of quantum entanglement from an octonionic fundamental model. The key observation is that thealgebra of octonions is non-associative, so that the associatorA(x,y,z) := (xy)z −x(yz)(1)provides a genuine trilinear measure of non-associativity. This immediately implies that afundamental coupling responsible for entanglement cannot be purely bipartite at the octonionic level. Instead, the minimal nontrivial coupling necessarily involves three degrees offreedom: one field for subsystem A, one field for subsystem B, and an additional mediatingoctonionic degree of freedom Ξ. We show that the resulting action naturally contains a termof the formλ∥A(ΨA,Ξ,ΨB)∥2,(2)which is structurally non-separable and therefore induces coupled equations of motion. Afterprojection onto an effective associative sector, this term appears as an entangling Hamiltonian on a Hilbert space HA ⊗ HB. We then prove step by step that such a Hamiltoniandynamically generates non-factorizable states from initial product states. A two-qubit example is worked out explicitly, including the reduced density matrix, entanglement entropy,and Bell—CHSH violation. The central conclusion is that, in this framework, entanglementis the effective associative manifestation of a deeper non-associative octonionic correlationstructure