A measurement is presented of single-and double-differential dijet cross sections in diffractive deep-inelastic ep scattering at HERA using data collected by the H1 experiment corresponding to an integrated luminosity of 290 pb(-1). The investigated phase space is spanned by the photon virtuality in the range of 4 < Q(2) < 100GeV(2) and by the fractional proton longitudinal momentum loss x(P) < 0.03. The resulting cross sections are compared with next-to-leading order QCD predictions based on diffractive parton distribution functions and the value of the strong coupling constant is extracted.