A bstract The associated production of prompt J/ψ and Υ mesons in pp collisions at a centre-of-mass energy of $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 13 TeV is studied using LHCb data, corresponding to an integrated luminosity of 4 fb − 1 . The measurement is performed for J/ψ ( Υ ) mesons with a transverse momentum p T &lt; 10 (30) GeV/ c in the rapidity range 2 . 0 &lt; y &lt; 4 . 5. In this kinematic range, the cross-section of the associated production of prompt J/ψ and Υ (1 S ) mesons is measured to be 133 ± 22 ± 7 ± 3 pb, with a significance of 7 . 9 σ , and that of prompt J/ψ and Υ (2 S ) mesons to be 76 ± 21 ± 4 ± 7 pb, with a significance of 4 . 9 σ . The first uncertainty is statistical, the second systematic, and the third due to uncertainties on the used branching fractions. This is the first observation of the associated production of J/ψ and Υ (1 S ) in proton-proton collisions. Differential cross-sections are measured as functions of variables that are sensitive to kinematic correlations between the J/ψ and Υ (1 S ) mesons. The effective cross-sections of the associated production of prompt J/ψ and Υ mesons are obtained and found to be compatible with measurements using other particle productions.