81 pages, 31 figures.We study the possible holographic connection between the Regge limit in QCD and critical gravitational collapse of a perfect fluid in higher dimensions. We begin by analyzing the problem of critical gravitational collapse of a perfect fluid in any number of dimensions and numerically compute the associated Choptuik exponent in d=5, 6 and 7 for a range of values of the speed of sound of the fluid. Using continuous self-similarity as guiding principle, a holographic correspondence between this process and the phenomenon of parton saturation in high-energy scattering in QCD is proposed. This holographic connection relates strong gravitational physics in the bulk with (nonsupersymmetric) QCD at weak coupling in four dimensions.The work of C.G. has been partially supported by the Spanish DGI contract FPA2003-02877 and the CAM grant HEPHACOS P-ESP-00346. A.T. thanks the Marie Curie and the Freydoon Mansouri foundations for support, and the CERN Theory Group for hospitality. M.A.V.-M. acknowledges partial support from the Spanish Government Grants PA2005-04823, FIS2006-05319 and Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042), and thanks the CERN Theory Group for hospitality.