The acceleration of particles up to GeV or higher energies in microquasars has been the subject of considerable theoretical and observational efforts in the past few years . Sco X-1 is a microquasar from which evidence of highly energetic particles in the jet has been found when it is in the so-called Horizontal Branch ( HB ) , a state when the radio and hard X-ray fluxes are higher and a powerful relativistic jet is present . Here we present the first very high energy gamma-ray observations of Sco X-1 , obtained with the MAGIC telescopes . An analysis of the whole dataset does not yield a significant signal , with 95 % CL flux upper limits above 300 GeV at the level of 2.4 \times 10 ^ { -12 } \mathrm { cm ^ { -2 } s ^ { -1 } } . Simultaneous RXTE observations were conducted to provide the X-ray state of the source . A selection of the gamma-ray data obtained during the HB based on the X-ray colors did not yield a signal either , with an upper limit of 3.4 \times 10 ^ { -12 } \mathrm { cm ^ { -2 } s ^ { -1 } } . These upper limits place a constraint on the maximum TeV luminosity to non-thermal X-ray luminosity of L _ { \mathrm { VHE } } / L _ { \mathrm { ntX } } \lesssim 0.02 , that can be related to a maximum TeV luminosity to jet power ratio of L _ { \mathrm { VHE } } / L _ { \mathrm { j } } \lesssim 10 ^ { -3 } . Our upper limits indicate that the underlying high-energy emission physics in Sco X-1 must be inherently different from that of the hitherto detected gamma-ray binaries .