  We observed $\gamma$-ray burst (GRB) 221009A using very long baseline
interferomety (VLBI) with the European VLBI Network (EVN) and the Very Long
Baseline Array (VLBA), over a period spanning from 40 to 262 days after the
initial GRB. The high angular resolution (mas) of our observations allowed us,
for the second time ever, after GRB 030329, to measure the projected size, $s$,
of the relativistic shock caused by the expansion of the GRB ejecta into the
surrounding medium. Our observations support the expansion of the shock with a
$>4\sigma$-equivalent significance, and confirm its relativistic nature by
revealing an apparently superluminal expansion rate. Fitting a power law
expansion model, $s\propto t^a$, to the observed size evolution, we find a
slope $a=0.69^{+0.13}_{-0.14}$. Fitting the data at each frequency separately,
we find different expansion rates, pointing to a frequency-dependent behaviour.
We show that the observed size evolution can be reconciled with a reverse shock
plus forward shock, provided that the two shocks dominate the emission at
different frequencies and, possibly, at different times.
