We present infrared aperture-masking interferometry (AMI) observations of newly formed dust from the colliding winds of the massive binary Wolf–Rayet system WR 137 with JWST using the Near Infrared Imager and Slitless Spectrograph (NIRISS). NIRISS AMI observations of WR 137 and a point-spread function calibrator star, HD 228337, were taken using the F380M and F480M filters in 2022 July and August as part of the Director's Discretionary Early Release Science program #1349. Interferometric observables (squared visibilities and closure phases) from the WR 137 "interferogram" were extracted and calibrated using three independent software tools: ImPlaneIA, AMICAL, and SAMpip. The analysis of the calibrated observables yielded consistent values except for slightly discrepant closure phases measured by ImPlaneIA. Based on all three sets of calibrated observables, images were reconstructed using three independent software tools: BSMEM, IRBis, and SQUEEZE. All reconstructed image combinations generated consistent images in both F380M and F480M filters. The reconstructed images of WR 137 reveal a bright central core with a ∼300 mas linear filament extending to the northwest. A geometric colliding-wind model with dust production constrained to the orbital plane of the binary system and enhanced as the system approaches periapsis provided a general agreement with the interferometric observables and reconstructed images. Based on a colliding-wind dust condensation analysis, we suggest that dust formation within the orbital plane of WR 137 is induced by enhanced equatorial mass loss from the rapidly rotating O9 companion star, whose axis of rotation is aligned with that of the orbit.