Since its first observation in the 1970s, neutrino-induced neutral-current single positive pion production ( NC 1 π + ) has remained an elusive and poorly understood interaction channel. This process is a significant background in neutrino oscillation experiments and studying it further is critical for the physics program of next-generation accelerator-based neutrino oscillation experiments. In this Letter, we present the first double-differential cross-section measurement of NC 1 π + interactions using data from the ND280 detector of the T2K experiment collected in ν -beam mode. The measured flux-averaged integrated cross section is σ = ( 6.07 ± 1.22 ) × 10 − 41     cm 2 / nucleon . We compare the results on a hydrocarbon target to the predictions of several neutrino interaction generators and final-state-interaction models. While model predictions agree with the differential results, the data show a weak preference for a cross-section normalization approximately 30% higher than predicted by most models studied in this Letter.