  We use data from M87* central black hole shadow, as well as from the S2 star
observations, in order to extract constraints on Barrow entropy. The latter is
a modified entropy arising from quantum-gravitational effects on the black hole
horizon, quantified by the new parameter $\Delta$. Such a change in entropy
leads to a change in temperature, as well as to the properties of the black
hole and its shadow. We investigate the photon sphere and the shadow of a black
hole with Barrow entropy, and assuming a simple model for infalling and
radiating gas we estimate the corresponding intensity. Furthermore, we use the
radius in order to extract the real part of the quasinormal modes, and for
completeness we investigate the spherical accretion of matter onto the black
hole, focusing on isothermal and polytropic test fluids. We extract the allowed
parameter region, and by applying a Monte-Carlo-Markov Chains analysis we find
that $ \Delta \simeq 0.0036^{+0.0792}_{-0.0145}$. Hence, our results place the
upper bound $\Delta\lesssim0.0828$ at 1$\sigma$, a constraint that is less
strong than the Big Bang Nucleosynthesis one, but significantly stronger than
the late-time cosmological constraints.
