We determine the low-field ordered magnetic phases of the S = 1 dimerized antiferromagnet Ba$_3$Mn$_2$O$_8$ using single-crystal neutron diffraction. We find that for magnetic fields between $\mu_0$$H$ = 8.80 T and 10.56 T applied along the [1$\bar 1$0] direction the system exhibits spin density wave order with incommensurate wave vectors of type ($\eta$,$\eta$,$\epsilon$). For $\mu_0$$H$ > 10.56 T, the magnetic order changes to a spiral phase with incommensurate wave vectors only along the [$hh$0] direction. For both field-induced ordered phases, the magnetic moments are lying in the plane perpendicular to the field direction. The nature of these two transitions is fundamentally different: the low-field transition is a second-order transition to a spin density wave ground state, while the one at higher field, toward the spiral phase, is of first order.