Although the response of plants exposed to severe drought stress has been studied extensively, little is known about how plants adapt their growth under mild drought stress conditions. Here, we analyzed the leaf and rosette growth response of six Arabidopsis (Arabidopsis thaliana) accessions originating from different geographic regions when exposed to mild drought stress. The automated phenotyping platform WIWAM was used to impose stress early during leaf development, when the third leaf emerges from the shoot apical meristem. Analysis of growth-related phenotypes showed differences in leaf development between the accessions. In all six accessions, mild drought stress reduced both leaf pavement cell area and number without affecting the stomatal index. Genome-wide transcriptome analysis (using RNA sequencing) of early developing leaf tissue identified 354 genes differentially expressed under mild drought stress in the six accessions. Our results indicate the existence of a robust response over different genetic backgrounds to mild drought stress in developing leaves. The processes involved in the overall mild drought stress response comprised abscisic acid signaling, proline metabolism, and cell wall adjustments. In addition to these known severe drought-related responses, 87 genes were found to be specific for the response of young developing leaves to mild drought stress.