Dialogue State Tracking (DST) forms a core component of automated chatbot based systems designed for specific goals like hotel, taxi reservation, tourist information etc. With the increasing need to deploy such systems in new domains, solving the problem of zero/few-shot DST has become necessary. There has been a rising trend for learning to transfer knowledge from resource-rich domains to unknown domains with minimal need for additional data. In this work, we explore the merits of meta-learning algorithms for this transfer and hence, propose a meta-learner D-REPTILE specific to the DST problem. With extensive experimentation, we provide clear evidence of benefits over conventional approaches across different domains, methods, base models and datasets with significant (5-25%) improvement over the baseline in a low-data setting. Our proposed meta-learner is agnostic of the underlying model and hence any existing state-of-the-art DST system can improve its performance on unknown domains using our training strategy.