The dark photon A^{'} and the dark Higgs boson h^{'} are hypothetical particles predicted in many dark sector models. We search for the simultaneous production of A^{'} and h^{'} in the dark Higgsstrahlung process e^{+}e^{-}→A^{'}h^{'} with A^{'}→μ^{+}μ^{-} and h^{'} invisible in electron-positron collisions at a center-of-mass energy of 10.58 GeV in data collected by the Belle II experiment in 2019. With an integrated luminosity of 8.34 fb^{-1}, we observe no evidence for signal. We obtain exclusion limits at 90% Bayesian credibility in the range of 1.7-5.0 fb on the cross section and in the range of 1.7×10^{-8}-200×10^{-8} on the effective coupling ε^{2}×α_{D} for the A^{'} mass in the range of 4.0 GeV/c^{2}<9.7 GeV/c^{2} and for the h^{'} mass M_{h^{'}}
