ABSTRACT We present the first characterization of the circumgalactic medium of Ly α emitters (LAEs), using a sample of 96 z ≈ 3.3 LAEs detected with the VLT/MUSE in fields centred on eight bright background quasars. The LAEs have low Ly α luminosities ($\sim 10^{42}\, \text{erg}\, \text{s}^{-1}$) and star formation rates (SFRs) $\sim 1~\text{M}_\odot \, \text{yr}^{-1}$, which for main-sequence galaxies correspond to stellar masses of only $\sim 10^{8.6}\, \text{M}_\odot$. The median transverse distance between the LAEs and the quasar sightlines is 165 proper kpc (pkpc). We stacked the high-resolution quasar spectra and measured significant excess H i and C iv absorption near the LAEs out to 500 $\text{km}\, \text{s}^{-1}$ and at least ≈250 pkpc (corresponding to ≈7 virial radii). At $\lesssim 30~\text{km}\, \text{s}^{-1}$ from the galaxies, the median H i and C iv optical depths are enhanced by an order of magnitude. The absorption is significantly stronger around the ≈1/3 of our LAEs that are part of ‘groups’, which we attribute to the large-scale structures in which they are embedded. We do not detect any strong dependence of either the H i or C iv absorption on transverse distance (over the range ≈50–250 pkpc), redshift, or the properties of the Ly α emission line (luminosity, full width at half-maximum, or equivalent width). However, for H i, but not C iv, the absorption at $\lesssim 100\, \text{km}\, \text{s}^{-1}$ from the LAE does increase with the SFR. This suggests that LAEs surrounded by more H i tend to have higher SFRs.