  The phase transition responsible for axion dark matter production can create
large amplitude isocurvature perturbations which collapse into dense objects
known as axion miniclusters. We use microlensing data from the EROS survey, and
from recent observations with the Subaru Hyper Suprime Cam to place constraints
on the minicluster scenario. We compute the microlensing event rate for
miniclusters treating them as spatially extended objects with an extended mass
function. Using the published bounds on the number of microlensing events we
bound the fraction of DM collapsed into miniclusters, $f_{\rm MC}$. For an
axion with temperature dependent mass consistent with the QCD axion we find
$f_{\rm MC}<0.22(m_a/100\,\mu\text{eV})^{-0.57}$, which represents the first
observational constraint on the minicluster fraction. We forecast that a
high-efficiency observation of ten nights with Subaru would be sufficient to
constrain $f_{\rm MC}\lesssim 0.1$ over the entire QCD axion mass range. We
make various approximations to derive these constraints and dedicated analyses
by the observing teams of EROS and Subaru are necessary to confirm our results.
If accurate theoretical predictions for $f_{\rm MC}$ can be made in future then
microlensing can be used to exclude, or discover, the QCD axion. Further
details of our computations are presented in a companion paper.
