Despite low levels of vascular endothelial growth factor (VEGF)-A, the secretome of human Wharton’s jelly (WJ) mesenchymal stromal cells (MSCs) effectively promoted proangiogenic responses in vitro, which were impaired upon the depletion of small (~140 nm) extracellular vesicles (EVs). The isolated EVs shared the low VEGF-A profile of the secretome and expressed five microRNAs, which were upregulated compared to fetal dermal MSC-derived EVs. These upregulated microRNAs exclusively targeted the VEGF-A gene within 54 Gene Ontology (GO) biological processes, 18 of which are associated with angiogenesis. Moreover, 15 microRNAs of WJ-MSC-derived EVs were highly expressed (Ct value ≤ 26) and exclusively targeted the thrombospondin 1 (THBS1) gene within 75 GO biological processes, 30 of which are associated with the regulation of tissue repair. The relationship between predicted microRNA target genes and WJ-MSC-derived EVs was shown by treating human umbilical-vein endothelial cells (HUVECs) with appropriate doses of EVs. The exposure of HUVECs to EVs for 72 h significantly enhanced the release of VEGF-A and THBS1 protein expression compared to untreated control cells. Finally, WJ-MSC-derived EVs stimulated in vitro tube formation along with the migration and proliferation of HUVECs. Our findings can contribute to a better understanding of the molecular mechanisms underlying the proangiogenic responses induced by human umbilical cord-derived MSCs, suggesting a key regulatory role for microRNAs delivered by EVs.