Magnetic Resonance Fingerprinting (MRF) estimates simultaneous, multi-parametric maps from a dynamic series of highly undersampled time-point images. At very high undersampling factors, some of these artefacts may propagate into the parametric maps leading to errors. Here we propose the use of locally low rank regularization for a low rank approximation reconstruction to enable highly accelerated MRF. The proposed approach was evaluated in simulations and in-vivo brain acquisitions. Results show that the proposed approach enables accurate MRF reconstructions from ~600 time-point images with one radial spoke per time-point.