  We calculate the $\mu$- and \textit{y}-type spectral distortions of Cosmic
Microwave Background (CMB), taking a non-standard interaction between baryons
and viscous dark matter. Using the CMB spectral distortion observations, we can
constrain any exotic mechanism that may change the energy of the CMB photon,
leading to a CMB spectrum distortion. Depending on the viscosity of dark
matter, the energy transfer between dark matter and baryons may modify, leading
to a modification in CMB distortion. The existing Cosmic Background Explorer
(COBE)/FIRAS and the Primordial Inflation Explorer (PIXIE) set limits on
\textit{y} and $\mu$ types of distortions to $y = 1.5\times10^{-5}$, $\mu =
9.0\times10^{-5}$ and $y = 10^{-8}$, $\mu = 5.0\times10^{-8}$, respectively. In
this paper, we discuss the pre-recombination contributions to $\mu$ and
\textit{y}-type distortions by viscous dark matter and constrain the parameter
space using PIXIE bounds on spectral distortion.
