The high temporal variability of wind power generation represents a major challenge for the realization of a sustainable energy supply. Large backup and storage facilities are necessary to secure the supply in periods of low renewable generation, especially in countries with a high share of renewables. We show that strong climate change is likely to impede the system integration of intermittent wind energy. To this end, we analyze the temporal characteristics of wind power generation based on high-resolution climate projections for Europe and uncover a robust increase of backup energy and storage needs in most of Central, Northern and North-Western Europe. This effect can be traced back to an increase of the likelihood for long periods of low wind generation and an increase in the seasonal wind variability.