This study pioneers the development of an automatic speech recognition (ASR) system for the Malasar language, an extremely low-resource ethnic language spoken by a tribal community in the Western Ghats of South India. Malasar is primarily an oral language which does not have a native script. Therefore, Malasar is often transcribed in Tamil script, a closely related major language. This work presents the first ever effort of leveraging the capabilities of multilingual transfer learning for recognising malasar speech. We fine-tune a pre-trained multilingual transformer model with Malasar speech data. In our endeavour to fine-tune this model using a Malasar speech corpus, we could successfully bring down the WER to 48.00% from 99.08% (zero shot baseline). This work demonstrates the efficacy of multilingual transfer learning in addressing the challenges of ASR for extremely low-resource languages, contributing to the preservation of their linguistic and cultural heritage.