Magnetohydrodynamic (MHD) phenomena play a crucial role in the design and operation of nuclear fusion reactors, both for the plasma and for electrically conducting fluids such as those in the blanket, whose dynamics are influenced by the magnetic field from the reactor core, which may vary in shape and intensity. The numerical simulation of MHD scenarios requires the resolution of highly nonlinear, multiphysics systems of equations, with prohibitive computational costs for multi-query real-time or parametric applications. This work employs a data-driven approach for MHD state reconstruction that combines dimensionality reduction via Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED) [1], a neural network architecture designed to estimate the full-order spatio-temporal state from sparse time-series measurements of some observable quantity, including unseen parametric conditions. The SHRED approach is applied to two fusion-relevant MHD benchmarks of increasing complexity: a two-dimensional channel flow [2] and a three-dimensional channel configuration [3], both involving compressible lead–lithium flows subjected to thermal gradients, gravitational effects, and different magnetic field configurations. These test cases are representative of realistic multiphysics conditions expected in liquid-metal blanket applications. For efficient training, the original full-order dataset is pre-processed using SVD to obtain a reduced representation of the reference truth. For both benchmarks, SHRED uses as input temperature measurements, being the easiest field to measure, from three sensors; the output consists of the reconstruction of the complete state of velocity, pressure, and temperature. Results show that SHRED can accurately reconstruct the complete MHD state for previously unseen magnetic field profiles, with both different intensities and spatio-temporal shapes. This study constitutes the first application of SHRED to MHD systems and highlights its potential as an efficient, low-cost surrogate modelling strategy for fusion-relevant multiphysics problems, with promising implications for real-time state estimation, monitoring, and control.