The flat-spectrum radio quasar PKS 1441+25 at a redshift of z = 0.940 is detected between 40 and 250 GeV with a significance of 25.5σ using the MAGIC telescopes. Together with the gravitationally lensed blazar QSO B0218+357 (z = 0.944), PKS 1441+25 is the most distant very high energy (VHE) blazar detected to date. The observations were triggered by an outburst in 2015 April seen at GeV energies with the Large Area Telescope on board Fermi. Multi-wavelength observations suggest a subdivision of the high state into two distinct flux states. In the band covered by MAGIC, the variability timescale is estimated to be 6.4 ± 1.9 days. Modeling the broadband spectral energy distribution with an external Compton model, the location of the emitting region is understood as originating in the jet outside the broad-line region (BLR) during the period of high activity, while being partially within the BLR during the period of low (typical) activity. The observed VHE spectrum during the highest activity is used to probe the extragalactic background light at an unprecedented distance scale for ground-based gamma-ray astronomy.