  Neutral hydrogen (HI) intensity mapping is a promising technique to probe the
large-scale structure of the Universe, improving our understanding on the
late-time accelerated expansion. In this work, we first scrutinize how an
alternative cosmology, interacting Dark Energy, can affect the 21-cm angular
power spectrum relative to the concordance $\Lambda$CDM model. We re-derive the
21-cm brightness temperature fluctuation in the context of such interaction and
uncover an extra new contribution. Then we estimate the noise level of three
upcoming HI intensity mapping surveys, BINGO, SKA1-MID Band$\,$1 and Band$\,$2,
respectively, and employ a Fisher matrix approach to forecast their constraints
on the interacting Dark Energy model. We find that while $\textit{Planck}\,$
2018 maintains its dominion over early-Universe parameter constraints, BINGO
and SKA1-MID Band$\,$2 put complementary bounding to the latest CMB
measurements on dark energy equation of state $w$, the interacting strength
$\lambda_i$ and the reduced Hubble constant $h$, and SKA1-MID Band$\,$1 even
outperforms $\textit{Planck}\,$ 2018 in these late-Universe parameter
constraints. The expected minimum uncertainties are given by SKA1-MID
Band$\,$1+$\textit{Planck}\,$: $\sim 0.35\%$ on $w$, $\sim 0.27\%$ on $h$,
$\sim 0.61\%$ on HI bias $b_{\rm HI}$, and an absolute uncertainty of about
$3\times10^{-4}$ ($7\times10^{-4}$) on $\lambda_{1}$ ($\lambda_{2}$). Moreover,
we quantify the effect of increasing redshift bins and inclusion of
redshift-space distortions in updating the constraints. Our results indicate a
bright prospect for HI intensity mapping surveys in constraining interacting
Dark Energy, whether on their own or further by a joint analysis with other
measurements.
