We report the results of a deep photometric search for planets and brown dwarfs in the nearby young OB Upper Scorpius association. We obtained optical (I) and near-infrared (JK_s) images around nine very low-mass stars and brown dwarf member candidates of the association, covering a total area of 113 arcmin^2. Using a point spread function subtraction technique, we have searched for planetary-mass companions (0.002 M_&sun; < M < 0.013 M_&sun;) at separations as close as 3´´ from the targets. We have not found any brown dwarfs more massive than 0.030 M_&sun; at projected distances larger than 70 AU, or planets more massive than 0.007 M_&sun; at projected distances larger than 600 AU. We set an upper limit of 20% (confidence level 68.3%) to the fraction of very low-mass stars and massive brown dwarfs with planetary mass companions (M > 0.007 M_&sun;) at physical distances larger than 600 AU. From the J, I-J colour-magnitude diagrams and follow-up K_s-band photometry, we identify four very red objects (I-J > 2.5) in the area of the survey. According to their positions in the diagram, below the expected theoretical sequence of the cluster, three are probable late M-dwarfs in the field. The faintest and reddest object (J-Ks = 2.39 ± 0.06) may be either a field intermediate L-dwarf with anomalously red J-Ks colour at a distance of ~135 pc, an extremely red distant galaxy, or a reddened planetary-mass object in the Upper Scorpius association.