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Paleoclimate proxies reveal abrupt transitions of the North Atlantic climate during past glacial intervals known as Dansgaard-Oeschger (DO) events. A central feature of DO events is a sudden warming of about 10°C in Greenland marking the beginning relatively mild phases termed interstadials. These exhibit gradual cooling over several hundred to a few thousand years until a final abrupt decline brings the temperatures back to cold stadial levels. As of now, the exact mechanism behind this millennial-scale variability remains inconclusive. Here, we propose an excitable model to explain Dansgaard-Oeschger cycles, where interstadials occur as noise-induced state space excursions. Our model comprises the mutual multi-scale interactions between four dynamical variables representing Arctic atmospheric temperatures, Nordic Seas’ temperatures and sea ice cover, and the Atlantic Meridional Overturning Circulation. The model’s atmosphere-ocean heat flux is moderated by the sea ice, which in turn is subject to large perturbations dynamically generated by fast evolving intermittent noise. If supercritical, perturbations trigger interstadial-like state space excursions during which all four model variables undergo qualitative changes that consistently resemble the signature of interstadials in corresponding proxy records. As a physical intermittent process generating the noise we propose convective events in the ocean or atmospheric blocking events. Our model accurately reproduces the DO cycle shape, return times and the dependence of the interstadial and stadial durations on the background conditions. In contrast to the prevailing understanding that DO variability is based on bistability in the underlying dynamics, we show that multi-scale, monostable excitable dynamics provides a promising alternative to explain millennial-scale climate variability associated with DO events.