We report on two XMM-Newton observations of the bright narrow-line Seyfert 1 galaxy Ark 564 taken 1 yr apart (2000 June and 2001 June). The 0.6-10 keV continuum is well described by a soft blackbody component (kT~ 140-150 eV) plus a steep power law (?~ 2.50-2.55). No significant spectral changes are observed between the two observations, although the X-ray flux in the second observation is ~40-50 per cent lower. In both observations, we detect a significant absorption edge at a rest-frame energy of ~0.73 keV, corresponding to O VII. The presence of the absorption feature is confirmed by a simultaneous Chandra grating observation in 2000 June, although the best-fitting edge threshold is at a slightly lower energy in the Chandra data, possibly because of a different parametrization of the underlying X-ray continuum. We find tentative evidence for a broad iron emission line in the 2000 June observation. The results from an analysis of the power spectral density (PSD) function are also presented. The present XMM-Newton data support the idea that the PSD shows two breaks, although the location of the high-frequency break requires further constraints.