The production of a 𝑍 boson in association with a 𝐽/𝜓 meson in proton–proton collisions probes the production mechanisms of quarkonium and heavy flavour in association with vector bosons, and allows studies of multiple parton scattering. Using 20.3fb−1 of data collected with the ATLAS experiment at the LHC in 𝑝𝑝 collisions at 𝑠√=8TeV , the first measurement of associated 𝑍+𝐽/𝜓 production is presented for both prompt and non-prompt 𝐽/𝜓 production, with both signatures having a significance in excess of 5𝜎 . The inclusive production cross-sections for 𝑍 boson production (analysed in 𝜇+𝜇− or 𝑒+𝑒− decay modes) in association with prompt and non-prompt 𝐽/𝜓(→𝜇+𝜇−) are measured relative to the inclusive production rate of 𝑍 bosons in the same fiducial volume to be (36.8±6.7±2.5)×10−7 and (65.8±9.2±4.2)×10−7 respectively. Normalised differential production cross-section ratios are also determined as a function of the J\uppsi transverse momentum. The fraction of signal events arising from single and double parton scattering is estimated, and a lower limit of 5.3 (3.7)mb at 68 (95)% confidence level is placed on the effective cross-section regulating double parton interactions.