Collective excitations of long-lived atomic hyperfine states can be synthesized into a Bose-Hubbard model in momentum space, where a spatially long-range interaction is introduced by laser-dressing the hyperfine state to Rydberg states. We explore stationary and dynamical properties of the momentum-space lattice in an artificial magnetic field. The many-body ground states support both chiral and anti-chiral edge currents in momentum space. Their stability against strong interactions is verified by a dynamical mean-field simulation. We show that the interplay of the interaction and chirality leads to correlated chiral dynamics, where an interaction-induced excitation blockade in momentum space suppresses the edge currents. When incorporating an effective decay to the lattice, we find that excitation transportation, whose dynamics is governed by a dissipative Bose-Hubard model, can be prohibited by a strong local dissipation, as a result of the quantum Zeno effect. Our study paves the route to quantum simulate topological phases and exotic dynamics with collective states of interacting atoms in momentum-space lattice.