We report a neutron diffraction study of single-crystal CePtAl$_3$ complemented by measurements of the specific heat under applied magnetic field. Below $T_\mathrm{N}$=3 K CePtAl$_3$ develops incommensurate antiferromagnetic order with a single modulation vector $\vec{k}$=$(0.676 \, 0 \, 0)$. Residual magnetic scattering intensity above $T_\mathrm{N}$ and a broadening of the specific heat anomaly at $T_\mathrm{N}$ may be consistently described in terms of a Gaussian distribution of transition temperatures with a standard deviation $σ≈0.5\,{\rm K}$. The distribution of $T_\mathrm{N}$ may be attributed to the observation of occupational and positional disorder between the Pt and Al sites. Measurements under magnetic field reveal unusual changes of the domain populations when the field is applied along the $[0\,1\,0]$ direction consistent with a transition from cycloidal to amplitude modulated magnetic order around 2.5 T.