Drought is one of the key natural hazards impacting net primary production and tree growth in forest ecosystems. Nonetheless, tree species show different responses to drought events, which make it difficult to adopt fixed tools for monitoring drought impacts under contrasting environmental and climatic conditions. In this study, we assess the response of forest growth and a satellite proxy of the net primary production (NPP) to drought in peninsular Spain and the Balearic Islands, a region characterized by complex climatological, topographical, and environmental characteristics. Herein, we employed three different indicators based on in situ measurements and satellite image-derived vegetation information (i.e., tree-ring width, maximum annual greenness, and an indicator of NPP). We used seven different climate drought indices to assess drought impacts on the tree variables analyzed. The selected drought indices include four versions of the Palmer Drought Severity Index (PDSI, Palmer Hydrological Drought Index (PHDI), Z-index, and Palmer Modified Drought Index (PMDI)) and three multi-scalar indices (Standardized Precipitation Evapotranspiration Index (SPEI), Standardized Precipitation Index (SPI), and Standardized Precipitation Drought Index (SPDI)). Our results suggest that—irrespective of drought index and tree species—tree-ring width shows a stronger response to interannual variability of drought, compared to the greenness and the NPP. In comparison to other drought indices (e.g., PDSI), and our results demonstrate that multi-scalar drought indices (e.g., SPI, SPEI) are more advantageous in monitoring drought impacts on tree-ring growth, maximum greenness, and NPP. This finding suggests that multi-scalar indices are more appropriate for monitoring and modelling forest drought in peninsular Spain and the Balearic Islands.