We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI) gravity. We show that this bound depends on an energy condition controlled by the model parameter $kappa$. From this bound, we can constrain $kappalesssim 10^{8}text{m}^2$ if a neutron star with a mass around $3M_{odot}$ is observed in the future. In addition, to avoid the potential pathologies in EiBI, a emph{Hagedorn-like} equation of state associated with $kappa$ at the center of a compact star is inevitable, which is similar to the Hagedorn temperature in string theory.
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