Despite past efforts, a comprehensive theory of massive star formation is still lacking. One of the most remarkable properties of massive stars is that almost all of them are found in binaries or higher-order multiple systems. Since multiplicity is an important outcome parameter of a star formation process, observations that cover the full companion mass ratio and separation regime are essential to constrain massive star formation theories. We aim to characterise the multiplicity properties of 20 OB stars (one of which turned out to be a foreground object) in the active star-forming region Sco OB1 in the separation range 0.15"-6" (~200-9000AU), using high- contrast imaging observations. These observations enabled us to reach very large magnitude differences and explore an as of yet uncharted territory of companions around massive stars. We used VLT/SPHERE to simultaneously observe with IFS and IRDIS, obtaining high-contrast imaging observations that cover a field of view (FoV) of 1.73"x1.73" in YJH bands and 11"x12.5" in K1 and K2 bands, respectively. We extracted low-resolution IFS spectra of candidate companions within 0.85" and compared them with PHOENIX and ATLAS9 atmosphere models to obtain an estimate of their fundamental parameters. Furthermore, we retrieved an estimate of the mass and age of all sources in the larger IRDIS FoV. The observations reached contrast magnitudes of {Delta}K1-13 on average, so we were able to detect sources at the stellar-substellar boundary. In total, we detect 789 sources, most of which are likely background sources. Thirty objects that are estimated to be in the stellar mass regime have a 20% or lower probability of being spurious associations. We obtain SPHERE companion fractions of 2.3+/-0.4 and 4.2+/-0.8 for O- and B-type stars, respectively. Splitting the sample between more massive (>20M_{sun}_) and less massive stars (<20M_{sun}_), we obtain companion fractions of 2.3+/-0.4 and 3.9+/-0.7, respectively. Including all previously detected companions, we find a total multiplicity fraction of 0.89+/-0.07 for separations in the range of ~0-12000AU. With SPHERE, we are probing an unexplored area in the magnitude versus separation diagram of companions, which is crucial to achieve a complete overview of the multiplicity properties of massive stars and ultimately improve our understanding of massive star formation.