The Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes observed the BL Lac object H1722+119 (redshift unknown) for six consecutive nights between 2013 May 17 and 22, for a total of 12.5 h. The observations were triggered by high activity in the optical band measured by the KVA (Kungliga Vetenskapsakademien) telescope. The source was for the first time detected in the very high energy (VHE, E > 100 GeV) γ-ray band with a statistical significance of 5.9σ. The integral flux above 150 GeV is estimated to be (2.0 ± 0.5) per cent of the Crab nebula flux. We used contemporaneous high energy (HE, 100 MeV < E < 100 GeV) γ-ray observations from Fermi-Large Area Telescope to estimate the redshift of the source. Within the framework of the current extragalactic background light models, we estimate the redshift to be z = 0.34 ± 0.15. Additionally, we used contemporaneous X-ray to radio data collected by the instruments on board the Swift satellite, the KVA, and the Owens Valley Radio Observatory telescope to study multifrequency characteristics of the source. We found no significant temporal variability of the flux in the HE and VHE bands. The flux in the optical and radio wavebands, on the other hand, did vary with different patterns. The spectral energy distribution of H1722+119 shows surprising behaviour in the ˜3 × 1014-1018 Hz frequency range. It can be modelled using an inhomogeneous helical jet synchrotron self-Compton model.