We report the first systematic study of the electrical transport and magnetic properties of BaRu6O12, which has a quasi-one-dimensional (quasi-1D) hollandite structure. We show that BaRu6O12 is quasi-1D electronically as well. Its physical properties were found to be extremely sensitive to disorder. Furthermore, a transition from being metallic with a resistance drop around 2 K to being weakly insulating as the applied magnetic field was increased was also found. We propose that these two features are related to the possible presence of a quantum phase transition in this material system.