jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pThe production of jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) mesons in proton-lead collisions at a centre-of-mass energy per nucleon pair of jats:inline-formulajats:alternativesjats:tex-math$$ \sqrt{s_{\textrm{NN}}} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msqrt mml:msub mml:mis</mml:mi> mml:miNN</mml:mi> </mml:msub> </mml:msqrt> </mml:math></jats:alternatives></jats:inline-formula> = 8jats:italic.</jats:italic>16 TeV is studied with the LHCb detector using data corresponding to an integrated luminosity of 34 nbjats:supjats:italic−</jats:italic>1</jats:sup>. The prompt and nonprompt jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) production cross-sections and the ratio of the jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) to jats:italicJ/ψ</jats:italic> cross-section are measured as a function of the meson transverse momentum and rapidity in the nucleon-nucleon centre-of-mass frame, together with forward-to-backward ratios and nuclear modification factors. The production of prompt jats:italicψ</jats:italic>(2jats:italicS</jats:italic>) is observed to be more suppressed compared to jats:italicpp</jats:italic> collisions than the prompt jats:italicJ/ψ</jats:italic> production, while the nonprompt productions have similar suppression factors.</jats:p>