Human-induced climate change is considered a conspicuous threat to biodiversity in the 21st century. Species' response to climate change depends on their exposition, sensitivity and ability to adapt to novel climates. Exposure to climate change is however uneven within species' range, so that some populations may be more at risk than others. Identifying the regions most exposed to climate change is therefore a first and pivotal step on determining species' vulnerability across their geographic ranges. Here, we aimed at quantifying mammal local exposure to climate change across species' ranges. We identified areas in the Brazilian Amazon where mammals will be critically exposed to non-analogue climates in the future with different variables predicted by 15 global circulation climate forecasts. We also built a null model to assess the effectiveness of the Amazon protected areas in buffering the effects of climate change on mammals, using an innovative and more realistic approach. We found that 85% of species are likely to be exposed to non-analogue climatic conditions in more than 80% of their ranges by 2070. That percentage is even higher for endemic mammals; almost all endemic species are predicted to be exposed in more than 80% of their range. Exposure patterns also varied with different climatic variables and seem to be geographically structured. Western and northern Amazon species are more likely to experience temperature anomalies while northeastern species will be more affected by rainfall abnormality. We also observed an increase in the number of critically-exposed species from 2050 to 2070. Overall, our results indicate that mammals might face high exposure to climate change and that protected areas will probably not be efficient enough to avert those impacts.