Several lines of evidence suggest that the warming climate plays a vital role in driving certain types of extreme weather. The impact of warming and of extreme weather on forest carbon assimilation capacity is poorly known. Filling this knowledge gap is critical towards understanding the amount of carbon that forests can hold. Here, we used a perfect-deficit approach to identify forest canopy photosynthetic capacity (CPC) deficits and analyze how they correlate to climate extremes, based on observational data measured by the eddy covariance method at 27 forest sites over 146 site-years. We found that droughts severely affect the carbon assimilation capacities of evergreen broadleaf forest (EBF) and deciduous broadleaf forest. The carbon assimilation capacities of Mediterranean forests were highly sensitive to climate extremes, while marine forest climates tended to be insensitive to climate extremes. Our estimates suggest an average global reduction of forest CPC due to unfavorable climate extremes of 6.3 Pg C (~5.2% of global gross primary production) per growing season over 2001–2010, with EBFs contributing 52% of the total reduction.