ABSTRACT We derive the maximum fraction of energy emitted in the form of massive (Kaluza–Klein) gravitons by core collapse supernovae, and the corresponding minimal extra-dimensional Planck mass M* in the ADD gravity framework at TeV scales. Our constraints arise (a) from the extragalactic gamma-ray background observed by Fermi-LAT after astrophysical sources have been removed and (b) via the residual galactic emission left after astrophysical and potentially dark matter emission have been removed. We focus on a number of extra dimensions 3 and 4, since M* is then in the TeV range, where astrophysical and collider constraints compete. Lower limits on M* are derived in the case (a) of 8.0 and 1.1 TeV for n = 3 and n = 4, respectively, and in the case (b) of 16 and 1.9 TeV. These limits are especially robust and insensitive to the various uncertainties involved.