Despite the coupled nature of water and electricity demand, the two utilities are often managed by different entities with minimal interaction. Neglecting the water-energy demand nexus leads to to suboptimal management decisions, particularly under climate change. Here, we leverage state-of-the-art machine learning and contemporary climate analogs to project the city-level coupled water and electricity demand of 46 major U.S. cities into the future. The results show that many U.S. cities may experience an increase in electricity (water) demand of up to 20% (15%) due to climate change under a high emissions scenario, with a clear north-south gradient. In the absence of appropriate mitigation strategies, these changes will likely stress current infrastructure, limiting the effectiveness of the ongoing grid decarbonization efforts. In the event that cities are unable to match the increasing demand, there may be increased occurrence of supply shortages, leading to blackouts with disproportionate impacts on vulnerable populations. As such, reliable projections of future water and electricity demand under climate change are critical not only for preventing further exacerbation of the existing environmental injustices but also for more effective design and execution of climate change mitigation and adaptation plans.