We present the serendipitous discovery of eclipse-like events around the massive white dwarf SDSS J152934.98+292801.9 (hereafter J1529+2928). We selected J1529+2928 for time-series photometry based on its spectroscopic temperature and surface gravity, which place it near the ZZ Ceti instability strip. Instead of pulsations, we detect photometric dips from this white dwarf every 38 minutes. Follow-up optical spectroscopy observations with Gemini reveal no significant radial velocity variations, ruling out stellar and brown dwarf companions. A disintegrating planet around this white dwarf cannot explain the observed light curves in different filters. Given the short period, the source of the photometric dips must be a dark spot that comes into view every 38 minutes due to the rotation of the white dwarf. Our optical spectroscopy does not show any evidence of Zeeman splitting of the Balmer lines, limiting the magnetic field strength to B < 70 kG. Since up to 15% of white dwarfs display kG magnetic fields, such eclipse-like events should be common around white dwarfs. We discuss the potential implications of this discovery on transient surveys targeting white dwarfs, like the K2 mission and the Large Synoptic Survey Telescope. This work is based on observations obtained at the Gemini Observatory, McDonald Observatory, and the Apache Point Observatory 3.5-m telescope. The latter is owned and operated by the Astrophysical Research Consortium. Gemini Observatory is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).