  In theories with the large extra dimensions beyond the standard 4-dimensional
spacetime, axions could propagate in such extra dimensions, and acquire
Kaluza-Klein (KK) excitations. These KK axions are produced in the Sun and
could solve unexplained heating of the solar corona. While most of the solar KK
axions escape from the solar system, a small fraction is gravitationally
trapped in orbits around the Sun. They would decay into two photons inside a
terrestrial detector. The event rate is expected to modulate annually depending
on the distance from the Sun. We have searched for the annual modulation
signature using $832\times 359$ kg$\cdot$days of XMASS-I data. No significant
event rate modulation is found, and hence we set the first experimental
constraint on the KK axion-photon coupling of $4.8 \times 10^{-12}\,
\mathrm{GeV}^{-1}$ at 90% confidence level for a KK axion number density of
$\bar{n}_\mathrm{a} = 4.07 \times 10^{13}\, \mathrm{m}^{-3}$, the total number
of extra dimensions $n = 2$, and the number of extra dimensions $\delta = 2$
that axions can propagate in.
