The authors deal with the Fibonacci superlattices, a class of quasi-periodic metamaterials whose elementary cell is characterized by two elastic building blocks. The elementary cell (or Fibonacci word) is arranged according to the generalized Fibonacci sequence along a periodicity vector to generate a finite system endowed with a quasi-periodic microstructure. After determining the lagrangian model, the Floquet–Bloch decomposition and the tranfer matrix method are employed to derive the eigenproblem whose resolution leads to the derivation of the band structures for several generalized Fibonacci words characterized by a self-similar bahaviour. Then, a dynamic continualization approach is detailed to identify equivalent multi-field integral-type and gradient-type higher-order non-local continua by relying on the equivalence between the Z-transform of the vector containing nodal stress and displacement and the spatial Fourier transform with complex argument of the corresponding continuum fields and recasting the kernel as a truncated Taylor series. Finally, the homogenized band structures are compared with those given by the Floquet–Bloch theory and an excellent agreement is observed.