Nordic welfare states have well institutionalised practises of gathering health and social wellbeing data from their citizens. The establishment of population registers coincided with the building of welfare state institutions and a social contract relying on solidarity. During the last decade, the significance of Nordic registers and health data has increased and they have become sources of economic value. Recent policies expect registers, health data and biobanks to attract international investments, making Nordic countries world-leaders in the global health data economy. In this article we question the conditions and boundaries of solidarity in the emerging data-driven health economy. We argue that the logics of welfare state and data-driven health economy create a paradox - the data economy is not possible without the welfare state data regime, but the logic of data-driven health economy contradicts the value bases of the welfare state data regime and therefore the justifications for data gathering and use become questionable. We develop the concept of solidarization to describe the process by which individuals are expected to behave in a solidaristic way to support data gathering and related policy processes. We demonstrate the solidarity paradox through a recent legislative and data infrastructure reform in Finland and discuss it in relation to academic literature on solidarity.