In this paper, we study the implications of the modular A4 flavor symmetry in constructing a supersymmetric minimal type-(I+II) seesaw model, in which only one right-handed neutrino and two Higgs triplets are introduced to account for the tiny neutrino masses, flavor mixing and CP violation. We consider the most economical case where the right-handed neutrino and the Higgs triplets in this model are assigned into the trivial one-dimensional irreducible representation of the modular group A4, and all the modular forms are with the lowest weights they can take. We find that the octant of the mixing angle θ23 strongly depends on the hierarchy of free model parameters in the charged-lepton sector. We also show that the neutrino mass matrix can possess an approximate μ−τ reflection symmetry for some specific values of free parameters. Moreover, our model predicts relatively large masses of three light neutrinos, thus can be easily tested in future neutrino experiments.