  With a dynamical mass of $3 \, M_\mathrm{Jup}$, the recently discovered giant
planet AF Lep b is the lowest-mass imaged planet with a direct mass
measurement. Its youth and spectral type near the L/T transition make it a
promising target to study the impact of clouds and atmospheric chemistry at low
surface gravities. In this work, we present JWST/NIRCam imaging of AF Lep b.
Across two epochs, we detect AF Lep b in F444W ($4.4 \, \mathrm{\mu m}$) with
S/N ratios of 9.6 and 8.7, respectively. At the planet's separation of $320 \,
\mathrm{mas}$ during the observations, the coronagraphic throughput is
${\approx}7\%$, demonstrating that NIRCam's excellent sensitivity persists down
to small separations. The F444W photometry of AF Lep b affirms the presence of
disequilibrium carbon chemistry and enhanced atmospheric metallicity. These
observations also place deep limits on wider-separation planets in the system,
ruling out $1.1 \, M_\mathrm{Jup}$ planets beyond $15.6 \, \mathrm{au}$ (0.58
arcsec), $1.1 \, M_\mathrm{Sat}$ planets beyond $27 \, \mathrm{au}$ (1 arcsec),
and $2.8 \, M_\mathrm{Nep}$ planets beyond $67 \, \mathrm{au}$ (2.5 arcsec). We
also present new Keck/NIRC2 $L'$ imaging of AF Lep b; combining this with the
two epochs of F444W photometry and previous Keck $L'$ photometry provides
limits on the long-term 3-$5 \, \mathrm{\mu m}$ variability of AF Lep b on
months-to-years timescales. AF Lep b is the closest-separation planet imaged
with JWST to date, demonstrating that planets can be recovered well inside the
nominal (50% throughput) NIRCam coronagraph inner working angle.
