We describe and report the status of a neutrino-triggered program in IceCube that generates real-time alerts for gamma-ray follow-up observations by atmospheric-Cherenkov telescopes (MAGIC and VERITAS). While IceCube is capable of monitoring the whole sky continuously, high-energy gamma-ray telescopes have restricted fields of view and in general are unlikely to be observing a potential neutrino-flaring source at the time such neutrinos are recorded. The use of neutrino-triggered alerts thus aims at increasing the availability of simultaneous multi-messenger data during potential neutrino flaring activity, which can increase the discovery potential and constrain the phenomenological interpretation of the high-energy emission of selected source classes (e.g. blazars). The requirements of a fast and stable online analysis of potential neutrino signals and its operation are presented, along with first results of the program operating between 14 March 2012 and 31 December 2015.