The Ordovician Period (485–443 Ma) is characterized by abundant evidence for continental-sized ice sheets. Modeling studies published so far require a sharp CO<sub>2</sub> drawdown to initiate this glaciation. They mostly used non-dynamic slab mixed-layer ocean models. Here, we use a general circulation model with coupled components for ocean, atmosphere, and sea ice to examine the response of Ordovician climate to changes in CO<sub>2</sub> and paleogeography. We conduct experiments for a wide range of CO<sub>2</sub> (from 16 to 2 times the preindustrial atmospheric CO<sub>2</sub> level (PAL)) and for two continental configurations (at 470 and at 450 Ma) mimicking the Middle and the Late Ordovician conditions. We find that the temperature-CO<sub>2</sub> relationship is highly non-linear when ocean dynamics are taken into account. Two climatic modes are simulated as radiative forcing decreases. For high CO<sub>2</sub> concentrations (≥ 12 PAL at 470 Ma and ≥ 8 PAL at 450 Ma), a relative hot climate with no sea ice characterizes the warm mode. When CO<sub>2</sub> is decreased to 8 PAL and 6 PAL at 470 and 450 Ma, a tipping point is crossed and climate abruptly enters a runaway icehouse leading to a cold mode marked by the extension of the sea ice cover down to the mid-latitudes. At 450 Ma, the transition from the warm to the cold mode is reached for a decrease in atmospheric CO<sub>2</sub> from 8 to 6 PAL and induces a ~9 °C global cooling. We show that the tipping point is due to the existence of a 95% oceanic Northern Hemisphere, which in turn induces a minimum in oceanic heat transport located around 40° N. The latter allows sea ice to stabilize at these latitudes, explaining the potential existence of the warm and of the cold climatic modes. This major climatic instability potentially brings a new explanation to the sudden Late Ordovician Hirnantian glacial pulse that does not require any large CO<sub>2</sub> drawdown.