  The origin of strong sodium absorption, which has been observed for a few
nearby Type Ia supernovae (SNe Ia), remains elusive. Here we analyse two
high-signal-to-noise, intermediate-resolution VLT/X-shooter spectra at epochs
$+$18 and $+$27 days past peak brightness of the strongly lensed and
multiply-imaged Type Ia SN 2016geu which exploded at a redshift of $z = 0.4$.
We show that SN 2016geu exhibits very strong, multiple Na I and Ca II
absorption lines with a large total Na I D restframe equivalent width of 5.2
$\pm$ 0.2 A, among the highest ever detected for a SN Ia and similar to only a
handful of nearby SNe Ia with extraordinary large Na I D EWs. The absorption
system is time-invariant and extends over a large velocity span $\sim$ 250 km
s$^{-1}$. The majority of the absorption is blueshifted relative to the
strongest component, while there are both blueshifted and redshifted components
relative to the systemic redshift of the galaxy. The column density ratios and
widths of the absorption lines indicate that the absorption likely arises from
a combination of interstellar dusty molecular clouds and circumgalactic in- and
outflowing material, rather than circumstellar matter around the SN.
