  The pseudo-magnetic field created by a non-uniform unaxial strain is
introduced into the antiferromagnetic honeycomb nanoribbons. The formation of
magnon pseudo-Landau levels, which appear from the upper end of the spectrum
and whose level spacings are proportional to the square root of the level
index, is revealed by the linear spin-wave theory. The antiferromagnetic order
is gradually weakened along the $y$-direction by the strain. At large enough
strength, the system is decoupled into isolated zigzag chains near the upper
boundary, and demonstrates one-dimensional magnetic property there. While the
quantum Monte Carlo simulations also predict such a transition, this exact
method gives a critical point deeper in the bulk. We also investigate the $XY$
antiferromagnetic honeycomb nanoribbons, and find similar pseudo-Landau levels
and antiferromagnetic evolution. Our results unveil the effect of a non-uniform
unaxial strain on the spin excitaions, and may be realized experimentally based
on two-dimensional quantum magnetic materials.
