RNA structure is critical for multiple steps in gene regulation. However, how structures of transcripts differ both within and between individual cells is unknown. Here, we develop a method enabling the simultaneous determination of transcript structure and abundance at single-cell resolution and apply it to human embryonic stem cells (hESCs) and differentiating neurons. Remarkably, RNA structure overall is more homogeneous in hESCs compared to neurons, with the greatest homogeneity found in coding regions. More extensive heterogeneity is found within 3’ UTRs and is determined by specific RNA binding proteins. Overall RNA structure profiles better discriminate cell type identity and differentiation stage than gene expression profiles alone. We further discover a cell-type variable region overlapping helix 44 of 18S rRNA that is associated with cell cycle and translation control. Our method thus opens the door to the systematic characterization of RNA structure-function relationships at single-cell resolution.