This paper presents a novel probabilistic machine learning (PML) framework to estimate the Brillouin frequency shift (BFS) from both Brillouin gain and phase spectra of a vector Brillouin optical time-domain analysis (VBOTDA). The PML framework is used to predict the Brillouin frequency shift (BFS) along the fiber and to assess its predictive uncertainty. We compare the predictions obtained from the proposed PML model with a conventional curve fitting method and evaluate the BFS uncertainty and data processing time for both methods. The proposed method is demonstrated using two BOTDA systems: (i) a BOTDA system with a 10 km sensing fiber and (ii) a vector BOTDA with a 25 km sensing fiber. The PML framework provides a pathway to enhance the VBOTDA system performance.