  We report new constraints on the size of large extra dimensions from data
collected by the MINOS experiment between 2005 and 2012. Our analysis employs a
model in which sterile neutrinos arise as Kaluza-Klein states in large extra
dimensions and thus modify the neutrino oscillation probabilities due to mixing
between active and sterile neutrino states. Using Fermilab's NuMI beam exposure
of $10.56 \times 10^{20}$ protons-on-target, we combine muon neutrino charged
current and neutral current data sets from the Near and Far Detectors and
observe no evidence for deviations from standard three-flavor neutrino
oscillations. The ratios of reconstructed energy spectra in the two detectors
constrain the size of large extra dimensions to be smaller than
$0.45\,\mu\text{m}$ at 90% C.L. in the limit of a vanishing lightest active
neutrino mass. Stronger limits are obtained for non-vanishing masses.
