  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 (IDE), 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 IDE 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}\,$: $\sim 0.34\%$ on $w$, $\sim 0.22\%$ on $h$,
$\sim 0.64\%$ 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 effects from systematics of the redshift bin number,
redshift-space distortions, foreground residuals and uncertainties on the
measured HI fraction, $\Omega_{\mathrm{HI}}(z)$. Our results indicate a bright
prospect for HI intensity mapping surveys in constraining IDE, whether on their
own or further by synergies with other measurements.
