  We discover a new type of multiple-$q$ state, "ripple state", in a frustrated
honeycomb-lattice Heisenberg antiferromagnet under magnetic fields. The ground
state has an infinite ring-like degeneracy in the wavevector space, exhibiting
a cooperative paramagnetic state, "ring-liquid" state. We elucidate that the
system exhibits the ripple state as a new low-temperature thermodynamic phase
via a second-order phase transition from the ring-liquid state, keeping the
ring-like spin structure factor. The spin texture in real space looks like a
"water ripple" and can induce a giant electric polarization vortex. Possible
relationship to the honeycomb-lattice compound, ${\rm
Bi_{3}Mn_{4}O_{12}(NO_{3})}$, is discussed.
