The prompt and non-prompt production cross-sections for ψ(2S) mesons are measured using 2.1 fb⁻¹ of pp collision data at a centre-of-mass energy of 7 TeV recorded by the ATLAS experiment at the LHC. The measurement exploits the ψ(2s) → J/ψ(→ μ⁺μ⁻ )π⁺π⁻ decay mode, and probes ψ(2S) mesons with transverse momenta in the range 10 ≤ p_T < 100 GeV and rapidity |y| < 2.0. The results are compared to other measurements of ψ(2S) production at the LHC and to various theoretical models for prompt and non-prompt quarkonium production.