"We are watching the situation and we will infuse whatever liquidity is needed to keep markets reasonably well behaved," Rajan told reporters here on the sidelines of an interactive industry meet organised by the business chamber Assocham.
The UK will vote tomorrow on whether to remain in the 28-nation European Union or to leave.
Britain's exit from the EU, or Brexit, is being debated globally as it could have implications for financial markets and exchange rates globally.
The RBI is maintaining a close vigil on developments, and will take all necessary steps including liquidity support to ensure orderly conditions in financial markets, it added.
Assocham has said the government must put in place a contingency plan to fight off volatility arising out of the referendum on Brexit, as it is bound to unnerve the global financial markets.