Motivated by the prediction of a high TeV luminosity we investigated whether the blazar 1ES 1727+502 (z = 0.055) is emitting very high energy (VHE, E > 100 GeV) γ rays. We observed the BL Lac object 1ES 1727+502 in stereoscopic mode with the two MAGIC telescopes for 14 nights between May 6th and June 10th 2011, for a total effective observing time of 12.6 h. To study the multiwavelength spectral energy distribution (SED), we used simultaneous optical R-band data from the KVA telescope, archival UV/optical and X-ray observations from instruments UVOT and XRT on board of the Swift satellite, and high energy (HE, 0.1 GeV-100 GeV) γ-ray data from the Fermi-LAT instrument. We detected, for the first time, VHE γ-ray emission from 1ES 1727+502 at a statistical significance of 5.5σ. The integral flux above 150 GeV is estimated to be (2.1 ± 0.4)% of the Crab nebula flux and the de-absorbed VHE spectrum has a photon index of (2.7 ± 0.5). No significant short-term variability was found in any of the wavebands presented here. We model the SED using a one-zone synchrotron self-Compton model obtaining parameters typical for this class of sources.