NGC 2419 is a peculiar Galactic globular cluster offset from the others in the size-luminosity diagram, and showing several chemical abundance anomalies. Here, we present Stromgren uvby photometry of the cluster. Using the gravity- and metallicity-sensitive c1 and m1 indices, we identify a sample of likely cluster members extending well beyond the formal tidal radius. The estimated contamination by cluster non-members is only one per cent, making our catalogue ideally suited for spectroscopic follow-up. We derive photometric [Fe/H] of red giants, and depending on which metallicity calibration from the literature we use, we find reasonable to excellent agreement with spectroscopic [Fe/H], both for the cluster mean metallicity and for individual stars. We demonstrate explicitly that the photometric uncertainties are not Gaussian and this must be accounted for in any analysis of the metallicity distribution function.