We report the detection of pulsed gamma-ray emission from the Geminga pulsar (PSR J0633+1746) between $15,$GeV and $75,$GeV. This is the first time a middle-aged pulsar has been detected up to these energies. Observations were carried out with the MAGIC telescopes between 2017 and 2019 using the low-energy threshold Sum-Trigger-II system. After quality selection cuts, $sim 80,$hours of observational data were used for this analysis. To compare with the emission at lower energies below the sensitivity range of MAGIC, $11$ years of Fermi-LAT data above $100,$MeV were also analysed. From the two pulses per rotation seen by Fermi-LAT, only the second one, P2, is detected in the MAGIC energy range, with a significance of $6.3,sigma$. The spectrum measured by MAGIC is well-represented by a simple power law of spectral index $Gamma= 5.62pm0.54$, which smoothly extends the Fermi-LAT spectrum. A joint fit to MAGIC and Fermi-LAT data rules out the existence of a sub-exponential cut-off in the combined energy range at the $3.6,sigma$ significance level. The power-law tail emission detected by MAGIC is interpreted as the transition from curvature radiation to Inverse Compton Scattering of particles accelerated in the northern outer gap.
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