Diffractive dissociation of nuclei (Be, Al, W) in collisions with 450 GeV/c protons, pA→pX, has been measured with the HELIOS spectrometer at the CERN Super Proton synchrotron. The dependence of the single-diffraction cross-section on the nuclear mass A can be parametrized as σSD mb×A0.35±0.02, showing the peripheral nature of the process. The differential cross-section dσSD=(3.8±0.3)mb ×A0.35±0.02, is exponential with the slope parameter, increasing from 6.2±0.4 (GeV/c)-2 for beryllium to 7.9±0.5 (GeV/c)-2 for tungsten. The slope parameter also increases with increasing mass MX of the diffractively produced state. The rapidity, multiplicity, and transverse-momentum distributions of the particles of the diffractively produced state X show a longitudinal phase-space population and are remarkably insensitive to the nuclear mass. This, together with the A1/3 dependence of σSD, suggests that the dominant process of nuclear diffractive excitation is the dissociation of single nucleons.