  We investigated the low-energy incommensurate (IC) magnetic fluctuations in
Sr$_2$RuO$_4$ by the high-resolution inelastic neutron scattering measurements
and random phase approximation (RPA) calculations. We observed a spin resonance
with energy of $\hbar\omega_\text{res}=0.56$~meV centered at a characteristic
wavevector $\mathbf{Q}_\text{res}=(0.3, 0.3, 0.5)$. The resonance energy
corresponds well to the superconducting gap $2\Delta=0.56$~meV estimated by the
tunneling spectroscopy. The spin resonance shows the $L$ modulation with a
maximum at around $L = 0.5$. The $L$ modulated intensity of the spin resonance
and our RPA calculations indicate that the superconducting gaps regarding the
quasi-one-dimensional $\alpha$ and $\beta$ sheets at the Fermi surfaces have
the horizontal line nodes. These results may set a strong constraint on the
pairing symmetry of Sr$_2$RuO$_4$. We also discuss the implications on possible
superconducting order parameters.
