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We measure the cross section for the process $e^+e^-\to\pi^+\pi^-\psi(2S)$
from threshold up to 8~GeV center-of-mass energy
using events containing initial-state radiation,
produced at the PEP-II $e^+e^-$ storage rings.
The study is based on 298~fb$^{-1}$ of data recorded with the BaBar
detector. A structure is observed in the cross-section not far above
threshold, near 4.32~GeV. This structure is not compatible with
the $Y(4260)$ previously reported by this experiment.
A single resonance is adequate to describe the cross-section
in the low-energy region ($<$5.7~GeV).
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