The metal-insulator transition of VO$_2$, which in equilibrium is associated with a structural phase transition, has been intensively studied for decades. In particular, it is challenging to disentangle the role of Mott physics from dimerization effects in the insulating phase. Femtosecond time-resolved experiments showed that optical excitations can induce a transient metallic state in the dimerized phase, which is distinct from the known equilibrium phases. In this study, we combine non-equilibrium cluster dynamical mean-field theory with realistic first principles modeling to clarify the nature of this laser-induced metallic state. We show that the doublon-holon production by laser pulses with polarization along the V-V dimers and the subsequent inter-orbital reshuffling of the photo-carriers leads to a population of orbital-mixed states and the filling of the gap. The photo-induced metal state is qualitatively similar to a hot electronic state in the dimerized structure, and does not involve a collapse of the Mott gap.