We study three astrophysical/cosmological consequences of nonminimal couplings to gravity in wavelike vector dark matter. In the nonrelativistic limit, the nonminimal coupling with the lowest mass dimension leads to effective self-interactions that affect the mass-radius relation of vector solitons, growth of linear perturbations during structure formation, and the speed of gravitational waves (GWs). Based on the success of cold dark matter on large-scale perturbations and the current limits on GW speed, we constrain the dark matter mass and nonminimal coupling strength to be within the range |ξ
1|/m
2 ≪ 1050 eV-2 and -3 × 1046 eV-2 ≲ ξ
2/m
2 ≲ 8 × 1048 eV-2.