Communications over power lines in the frequency range above 2 MHz, commonly referred to as broadband (BB) power line communications (PLC), is a central communications scenario for smart power grids. BB-PLC channels are characterized by a dominant colored non-Gaussian additive noise, as well as by periodic variations of the channel impulse response and the noise statistics, induced by the mains voltage. In this work we study the fundamental rate limits for multiple input-multiple output (MIMO) BB-PLC channels, modeled as periodic channels with additive non-Gaussian noise and finite memory. We present bounds on the capacity of these channels by exploiting a bijection with time-invariant MIMO channels of extended dimensions. We illustrate the resulting fundamental limits in a numerical analysis corresponding to practical MIMO BB-PLC channels.