Are small finance banks regulated by the RBI?

Yes, the Small Finance Banks are regulated by the Reserve Bank of India (RBI). Small finance banks are governed by Banking Regulation Act 1949, Reserve Bank of India Act, 1934 and various other acts. You can read about the Types of Banks in India – Category and Functions of Banks in India in the given link.

Further readings:

1. Granting License for Small Finance Banks by the Reserve Bank of India (RBI)
2. SIDBI – Small Industries Development Bank of India & its Functions