  Infrared spectroscopy has been developed significantly. In particular,
infrared photons can be measured with high spectral and angular resolution in
state-of-art spectrographs. They are sensitive to monochromatic photons due to
the decay and annihilation of particles beyond the Standard Model, such as dark
matter (DM), while suppressing background photons that form a continuous
spectrum. In this paper, we study the indirect detection of the DM decaying
into infrared light using infrared spectrographs. In particular, we show that
serious thermal and astrophysical noises can be overcome. As concrete examples,
the Warm INfrared Echelle spectrograph to Realize Extreme Dispersion and
sensitivity (WINERED) installed at the Magellan Clay 6.5m telescope and
Near-Infrared Spectrograph (NIRSpec) at the James Webb Space Telescope (JWST)
are discussed. We show that a few hours of measurements of a faint dwarf
spheroidal galaxy with WINERED (NIRSpec-like spectrograph) in the Magellan
telescope (JWST) can probe an axion-like particle DM in the mass range
$m_\phi=1.8 - 2.7\,$eV ($0.5-4\,$eV) with a photon coupling
$g_{\phi\gamma\gamma}\gtrsim 10^{-11}{\rm GeV}^{-1}$. Complemental approaches,
taking advantage of the high resolutions, such as the measurement of the
Doppler shift of the signal photon lines and the possible search of the DM
decay around the Milky Way galaxy center with Infrared Camera and Spectrograph
(IRCS) at 8.2m Subaru telescope, are also presented.
