A theoretical study of the effects of in‐plane magnetic fields on the interband optical absorption spectra of quasiperiodic GaAs–(Ga,Al)As Fibonacci superlattices is presented within the effective‐mass approximation. The electron‐envelope wave functions and magnetic subbands are obtained by an expansion in harmonic‐oscillator wave functions. The theoretical optical absorption spectra are calculated for magnetic fields related by integer powers of the golden mean &tgr;=(1+&sqrt;5)/2. It is unambiguously shown that, for magnetic‐field values scaled by &tgr;2n, the corresponding optical absorption spectra essentially exhibit a self‐similar behavior, with the width of the peaks increasing linearly with the field, in agreement with the experimental results by D. Toet, M. Potemski, Y. Y. Wang, J. C. Maan, L. Tapter, and K. Ploog [Phys. Rev. Lett.66, 2128 (1991)]. ©1995 American Institute of Physics.