  We generalize the concept of the spin-momentum locking to magnonic systems
and derive the formula to calculate the spin expectation value for one-magnon
states of general two-body spin Hamiltonians. We give no-go conditions for
magnon spin to be independent of momentum. As examples of the magnon
spin-momentum locking, we analyze a one-dimensional antiferromagnet with the
N\'eel order and two-dimensional kagome lattice antiferromagnets with the
120$^\circ$ structure. We find that the magnon spin depends on its momentum
even when the Hamiltonian has the $z$-axis spin rotational symmetry, which can
be explained in the context of a singular band point or a $U(1)$ symmetry
breaking. A spin vortex in momentum space generated in a kagome lattice
antiferromagnet has the winding number $Q=-2$, while the typical one observed
in topological insulator surface states is characterized by $Q=+1$. A magnonic
analogue of the surface states, the Dirac magnon with $Q=+1$, is found in
another kagome lattice antiferromagnet. We also derive the sum rule for $Q$ by
using the Poincar\'e-Hopf index theorem.
