  We have derived high spatial resolution metallicity maps covering $\sim$42
deg$^2$ across the Small Magellanic Cloud (SMC) in an attempt to understand its
metallicity distribution and gradients up to a radius of $\sim$ 4$^{\circ}$.
Using the near-infrared VISTA Survey of the Magellanic Clouds, our data cover a
thrice larger area compared with previous studies. We identify red giant branch
(RGB) stars in spatially distinct $Y, (Y-K_{\rm s})$ colour--magnitude
diagrams. In any of our selected subregions, the RGB slope is used as an
indicator of the average metallicity, based on calibration to metallicity using
spectroscopic data. The metallicity distribution across the SMC is unimodal and
can be fitted by a Gaussian distribution with a peak at [Fe/H] = $-$0.97 dex
($\sigma$[Fe/H] = 0.05 dex). We find evidence of a shallow gradient in
metallicity ($-0.031 \pm 0.005$ dex deg$^{-1}$) from the galactic centre to
radii of 2$^{\circ}$--2.5$^{\circ}$, followed by a flat metallicity trend from
$\sim$ 3.5$^{\circ}$ to 4$^{\circ}$. We find that the SMC's metallicity
gradient is radially asymmetric. It is flatter towards the East than to the
West, hinting at mixing and/or distortion of the spatial metallicity
distribution (within the inner 3$^{\circ}$), presumably caused by tidal
interactions between the Magellanic Clouds.

Astrophysics of Galaxies;Solar and Stellar Astrophysics