The indoor low-voltage power line network is characterized by highly irregular interferences, where background noise coexists with bursty impulsive noise originating from household appliances and switching events. Traditional noise models, which are considered monofractal models, often fail to reproduce the clustering, intermittency, and long-range dependence seen in measurement data. In this paper, a Multifractal Random Walk (MRW) framework tailored for Power Line Communication (PLC) noise modelling is developed. MRW is a continuous time limit process based on discrete time random walks with stochastic log-normal variance. As such, the formulated MRW framework introduces a stochastic volatility component that modulates Gaussian increments, thus generating heavy-tailed statistics and multifractal scaling laws which are consistent with the measured PLC noise data. Empirical validation is done through structure function analysis and covariance of log-amplitudes, both of which reveal scaling characteristics that align well with MRW simulated predictions. This proposed model captures both the bursty nature and correlation structure of impulsive PLC noise more effectively as compared to the conventional monofractal approaches, thereby providing a mathematically grounded framework for accurate noise generation and robust system-level performance evaluation of PLC networks.