RNA Velocity allows the inference of cellular differentiation trajectories from single-cell RNA sequencing (scRNA-seq) data. It would be highly interesting to study these differentiation dynamics in the spatial context of tissues. Estimating spatial RNA velocities is, however, limited by the inability to spatially capture spliced and unspliced mRNA molecules in high-resolution spatial transcriptomics. We present SIRV, a method to spatially infer RNA velocities at the single-cell resolution by enriching spatial transcriptomics data with the expression of spliced and unspliced mRNA from reference scRNA-seq data. We used SIRV to infer spatial differentiation trajectories in the developing mouse brain, including the differentiation of midbrain-hindbrain boundary cells and marking the forebrain origin of the cortical hem and diencephalon cells. Our results show that SIRV reveals spatial differentiation patterns not identifiable with scRNA-seq data alone. Additionally, we applied SIRV to mouse organogenesis data and obtained robust spatial differentiation trajectories. Finally, we verified the spatial RNA velocities obtained by SIRV using 10x Visium data of the developing chicken heart and MERFISH data from human osteosarcoma cells. Altogether, SIRV allows the inference of spatial RNA velocities at the single-cell resolution to facilitate studying tissue development.