Charmonium production by 350 GeV/ c negative pions incident on tungsten, copper and silicon has been studied in the WA92 experiment. J/ ψ and ψ′ mesons are identified through their decays into muon pairs and are selected in the Feynman-χ range χ F > 0. Inclusive J/ ψ and ψ′ cross-sections and J/ ψ differential cross-sections as functions of χ F and p T 2 are measured. Assuming the relation σ = σ 0 A α between the nuclear cross-section, σ, and the atomic mass, A, of a target nucleus, a fit to J/ ψ data for different targets yields α = 0.87 ± 0.05 ± 0.04. Taking α = 0.87, the cross-sections per nucleon for J/ ψ and ψ′ are σ 0 ( J/ ψ) = 216 ± 5 ± 13 nb and σ 0( ψ′) = 28 ± 8 ± 11 nb, and their ratio is σ 0 ( ψ′)/ σ 0( J/ ψ) = 0.13 ± 0.05 ± 0.01. The measurements of charmonium production are compared with results on open-charm production previously obtained in the same experiment. The ratio between the J/ ψ cross-section and the charmed-meson cross-section, relating to the same experimental conditions, is found to be σ 0(J/ψ)/σ 0(D D − ) = 1.75±0.05±0.15) × 10 −2 .