  The Calorimetric Electron Telescope (CALET), in operation on the
International Space Station since 2015, collected a large sample of cosmic-ray
iron over a wide energy interval. In this Letter a measurement of the iron
spectrum is presented in the range of kinetic energy per nucleon from 10
GeV$/n$ to 2.0 TeV$/n$ allowing the inclusion of iron in the list of elements
studied with unprecedented precision by space-borne instruments. The
measurement is based on observations carried out from January 2016 to May 2020.
The CALET instrument can identify individual nuclear species via a measurement
of their electric charge with a dynamic range extending far beyond iron (up to
atomic number $Z$ = 40). The energy is measured by a homogeneous calorimeter
with a total equivalent thickness of 1.2 proton interaction lengths preceded by
a thin (3 radiation lengths) imaging section providing tracking and energy
sampling. The analysis of the data and the detailed assessment of systematic
uncertainties are described and results are compared with the findings of
previous experiments. The observed differential spectrum is consistent within
the errors with previous experiments. In the region from 50 GeV$/n$ to 2
TeV$/n$ our present data are compatible with a single power law with spectral
index -2.60 $\pm$ 0.03.
