This paper investigates the three-dimensional magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) nanofluid with the thermal radiation, cross-diffusion and heat source effects along a stretching sheet. The effects of chemical reaction, thermophoresis and Brownian motion are also studied. We have applied suitable similarity variables and transformed the governing boundary layer equations into a system of non-linear ordinary differential equations. The present problem is solved numerically by R–K-based shooting technique. The variations of the velocity, temperature and concentration profiles are shown graphically and discussed in detail. The numerical results of skin friction coefficient, Nusselt and Sherwood numbers are presented in tabular form for different physical parameters. It is noticed that the Dufour and thermal radiation parameters decrease the temperature field and raise the concentration field. The rising values of Deborah number and magnetic field reduce the friction factors, Nusselt and Sherwood numbers. Heat source and chemical reaction parameters decline the Nusselt number and boost the Sherwood number. Also, noticed that the Dufour and Soret numbers enhance the Nusselt number but they decrease the Sherwood number. © 2021, The Author(s), under exclusive licence to EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.