We report the first ground-based detections of the shallow transit of the super-Earth exoplanet 55 Cnc e using a 2-meter-class telescope. Using differential spectrophotometry, we observed one transit in 2013 and another in 2014, with average spectral resolutions of ~700 and ~250, spanning the Johnson BVR photometric bands. We find a white-light planet-to-star radius ratio of 0.0190 -0.0027+0.0023 from the 2013 observations and 0.0200 -0.0018+0.0017 from the 2014 observations. The two datasets combined results in a radius ratio of 0.0198 -0.0014+0.0013. These values are all in agreement with previous space-based results. Scintillation noise in the data prevents us from placing strong constraints on the presence of an extended hydrogen-rich atmosphere. Nevertheless, our detections of 55 Cnc e in transit demonstrate that moderate-size telescopes on the ground will be capable of routine follow-up observations of super-Earth candidates discovered by the Transiting Exoplanet Survey Satellite (TESS) around bright stars. We expect it will be also possible to place constraints on the atmospheric characteristics of those planets by devising observational strategies to minimize scintillation noise.