Ocean planets are volatile rich planets, not present in our Solar System, which are dominated by deep, global oceans. Theoretical considerations and planet formation modeling studies suggest that extrasolar ocean planets should be a very common type of planet. One might therefore expect that low-mass ocean planets would be ideal candidates when searching for habitable exoplanets, since water is considered to be an essential requirement for life. However, a very large global ocean can also strongly influence the climate.The high pressure at the oceans bottom results in the formation of high-pressure water ice, separating the planetary crust from the liquid ocean and, thus, also from the atmosphere. In our study we, therefore, focus on the CO2 cycle between the atmosphere and the ocean which determines the atmospheric CO2 content. The atmospheric amount of CO2 is a fundamental quantity for assessing the potential habitability of the planet's surface because of its strong greenhouse effect, which determines the planetary surface temperature to a large degree.In contrast to the stabilising carbonate-silicate cycle regulating the long-term CO2 inventory of the Earth atmosphere, we find that the CO2 cycle on ocean planets is positive and has strong destabilising effects on the planetary climate. By using a chemistry model for oceanic CO2 dissolution and an atmospheric model for exoplanets, we show that the CO2 feedback cycle is severely limiting the potential habitability of ocean planets.