Food production on our planet is dominantly based on agricultural practices developed during stable Holocene climatic conditions. Although it is widely accepted that climate change perturbs these conditions, no systematic understanding exists on where and how the major risks for entering unprecedented conditions may occur. Here, we address this gap by introducing the concept of safe climatic space (SCS), which incorporates the decisive climatic factors of agricultural production: precipitation, temperature, and aridity. We show that a rapid and unhalted growth of greenhouse gas emissions (SSP5-8.5) could force 31% of the global food crop and 34% of livestock production beyond the SCS by 2081-2100. The most vulnerable areas are South and Southeast Asia and Africa's Sudano-Sahelian Zone, which have low resilience to cope with these changes. Our results underpin the importance of committing to a low-emissions scenario (SSP1-2.6), whereupon the extent of food production facing unprecedented conditions would be a fraction.