The Griffith criterion is rewritten to account for the propagation of a self-affine crack. It is shown that the stress-field singularity in the close vicinity of the crack tip involves an exponent -(${\mathit{d}}_{\mathit{F}}$-1)/2 instead of -1/2. Furthermore, the fracture toughness is shown to be related to the ratio of the maximum height ${\mathit{z}}_{\mathrm{max}}$ to the self-affine correlation length \ensuremath{\xi}.