In their youth, protoplanetary discs are expected to be massive and self-gravitating, which results in non-axisymmetric spiral structures. However recent observations of young protoplanetary discs with ALMA have revealed that discs with large-scale spiral structure are rarely observed in the midplane. Instead, axisymmetric discs with some also having ring & gap structures are more commonly observed. Using 3D SPH simulations, we show that planet-disc interactions are able to suppress the large-scale spiral structure of self-gravitating protoplanetary discs — potentially resolving this discrepancy between observations and theoretical predictions. We present mock ALMA continuum observations which show that in the absence of a planet, spiral arms due to gravitational instability are easily observed. Whereas in the presence of a giant planet, the spiral structures are suppressed by the migrating planet resulting in a largely axisymmetric disc with ring and gap structure. Our modelling of the gas kinematics shows that the planet’s presence could be inferred, for example, using optically thin 13C16O. We show that it’s not necessary to limit the gas mass of discs by assuming high dust-to-gas mass ratios to explain a lack of spiral features that would otherwise be expected in high mass discs.