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 $3times10^{-4}$ ($7times10^{-4}$) 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.
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