A significant problem in inertial confinement fusion is that the material interfaces in the converging flow are subject to the Richtmyer-Meshkov instability when they are impulsively accelerated. It has been demonstrated that this instability can be suppressed in magnetohydrodynamic (MHD) flows at least for flow configurations with rectangular geometry. In order to understand the flow induced by attempting such suppression in converging flow configurations, it is necessary first to investigate the underlying base-flows, the canonical versions of which correspond to converging cylindrical and spherical MHD Riemann problems. Here, we present the numerical solution to one such case: the cylindrical MHD Riemann problem shown below with a uniform initial magnetic field of strength β = 2 and a pressure ratio of three across the interface. The wave structure is initially characterised by two outward- and two inward-moving waves, but as the solution develops, discontinuities form along the waves, producing a more complex flow structure. We investigate the different flow structures, their formation times, and identify how the compression achieved at the centre of the implosion is affected by the magnetic field.