In a theory with linear confinement, such as QCD, the masses squared, m^2, of mesons with high spin S or high radial excitation number n are expected, from semiclassical arguments, to grow linearly with S and n. We show that this translates into a strong constraint on the INFRARED behavior of a putative 5-dimensional theory holographically dual to QCD (AdS/QCD). In the simplest model which obeys such a constraint we find m^2 ~ (n+S).