  In this work, we study the potential of the Cherenkov Telescope Array (CTA)
for the detection of Galactic dark matter (DM) subhalos. We focus on low-mass
subhalos that do not host any baryonic content and therefore lack any
multiwavelength counterpart. If the DM is made of weakly interacting massive
particles (WIMPs), these dark subhalos may thus appear in the gamma-ray sky as
unidentified sources. A detailed characterization of the instrumental response
of CTA to dark subhalos is performed, for which we use the {\it ctools}
analysis software and simulate CTA observations under different array
configurations and pointing strategies, such as the scheduled extragalactic
survey. This, together with information on the subhalo population as inferred
from N-body cosmological simulations, allows us to predict the CTA
detectability of dark subhalos, i.e., the expected number of subhalos in each
of the considered observational scenarios. In the absence of detection, for
each observation strategy we set competitive limits to the annihilation cross
section as a function of the DM particle mass, that are at the level of
$\langle\sigma v\rangle\sim4\times10^{-24}$ ($7\times10^{-25}$)
$\mathrm{cm^3s^{-1}}$ for the $b\bar{b}$ ($\tau^+\tau^-$) annihilation channel
in the best case scenario. Interestingly, we find the latter to be reached with
no dedicated observations, as we obtain the best limits by just accumulating
exposure time from all scheduled CTA programs and pointings over the first 10
years of operation. This way CTA will offer the most constraining limits from
subhalo searches in the intermediate range between $\sim 1-3$ TeV,
complementing previous results with \textit{Fermi}-LAT and HAWC at lower and
higher energies, respectively.
