We have extended {\tt MadGraph5_aMC@NLO} capabilities by implementing computations for asymmetric hadron-hadron collisions, including proton-nucleus, pion-hadron or nucleus-nucleus collisions in order to obtain a tool for automated perturbative computations of cross sections (or ratios of cross sections) in asymmetric reactions at next-to-leading (NLO) order in αSαS​ in collinear factorisation. This tool, like the original symmetric version of \texttt{MadGraph5\_aMC@NLO}, automatically computes cross sections for different factorisation and renormalisation scales and PDFs provided by the {\tt LHAPDF} library, thereby allowing for an easy assessment of the associated theoretical uncertainties. In this paper, we present the validation of our code using WW and ZZ boson production in ppPb collisions and Drell-Yan-pair production in πWπW collisions. We also illustrate the capabilities of the framework by providing cross section and nuclear modification factors with their uncertainties for the production of WW and ZZ bosons, charm and bottom quarks as well as associated production of bbˉ+H0bbˉ+H0 in ppPb collisions at the LHC.