The Javalambre VARiability Survey (J-VAR) is a photometric survey that is being carried out with the 0.8m Javalambre Auxiliary Survey Telescope, located at the Observatorio Astrofísico de Javalambre (Teruel, Spain), using a subset of seven filters from J-PLUS, covering the wavelength range 0.39─0.88 $\mu$m. The scientific objectives of J-VAR are three: characterization of variable stars, detection of supernovae, and detection and characterization of small Solar system objects (SSOs). The main goal of this work is to present the first catalogue of SSOs compiled from the first data release (DR1) of the J-VAR survey, consisting of observations for 101 fields (visited at least 11 times each). We used the ssos pipeline to analyse each epoch (which usually consists of 21 images, except for the high frequency cases) for all the fields in the J-VAR DR1, retrieving the SSOs detected in the survey images. We analysed more than 30 000 images, recovering 131 966 detections, corresponding to a total of 6579 individual Solar system small bodies, $\sim$95 per cent of which are located in the Main Belt. We present here two catalogues: individual detections and combined magnitudes. In addition, we show some preliminary results: analysis of colour─colour plots and comparison with the known spectral properties of asteroids, photospectra for some objects observed in all seven filters, and we present a method for constructing partial light curves for objects detected in the high frequency epochs. Finally, we discuss the survey's potential to discover unknown Solar system bodies.