We report on a search for the day-night asymmetry of the Be-7 solar neutrino rate measured by Borexino at the Laboratori Nazionali del Gran Sasso (LNGS), Italy. The measured value, Adn=0.001 +- 0.012 (stat) +- 0.007 (syst), shows the absence of a significant asymmetry. This result alone rejects the so-called LOW solution at more than 8.5 sigma. Combined with the other solar neutrino data, it isolates the Large Mixing Angle (LMA) -- MSW solution at DeltaChi2 > 190 without relying on the assumption of CPT symmetry in the neutrino sector. We also show that including the day-night asymmetry, data from Borexino alone restricts the MSW neutrino oscillations to the LMA solution at 90% confidence level.