This paper reports on the atomic hydrogen gas (HI) observations of the spiral galaxy NGC 1566 using the newly commissioned Australian Square Kilometre Array Pathfinder radio telescope. We measure an integrated HI flux density of 180.2 Jy km s(-1) emanating from this galaxy, which translates to an HI mass of 1.94 x 10(10) M-circle dot at an assumed distance of 21.3Mpc. Our observations show that NGC 1566 has an asymmetric and mildly warped HI disc. The HI-to-stellar mass fraction (M-HI/M-*) of NGC 1566 is 0.29, which is high in comparison with galaxies that have the same stellar mass (10(10.8) M-circle dot). We also derive the rotation curve of this galaxy to a radius of 50 kpc and fit different mass models to it. The NFW, Burkert, and pseudo-isothermal darkmatter halo profiles fit the observed rotation curve reasonably well and recover dark matter fractions of 0.62, 0.58, and 0.66, respectively. Down to the column density sensitivity of our observations (NHI = 3.7 x 10(19) cm(-2)), we detect no HI clouds connected to, or in the nearby vicinity of, the HI disc of NGC 1566 nor nearby interacting systems. We conclude that, based on a simple analytic model, ram pressure interactions with the IGM can affect the HI disc of NGC 1566 and is possibly the reason for the asymmetries seen in the HI morphology of NGC 1566.