Acharya is the second top RBI official to quit after Governor Urijit Patel's exit last December.
The sources said that Acharya, who joined as the RBI Deputy Governor in January 2017, was against the central bank's decision on repeated cuts of repo rates to support the government's public spending and consumption boost measures to tackle the slowing growth.
Acharya viewed such steps as putting fiscal discipline into risk and he did not want to be part of "those decisions", sources said.
The RBI, however, has not responded to queries on this regard, neither has Acharya made any statement as yet.
To spur the economy, the Rserve Bank of India (RBI) had cut repo rate by 25 bps to 5.75 per cent in June while switching to "accommodative" stance implying amenable to further cuts.
This is the third time on the trot that the six-member Monetary Policy Committee (MPC) has decided on a 25-basis points rate cut, making it a hat-trick of repo rate cuts.
The rate cut also comes in the backdrop of benign retail inflation. Following the MPC decision, the repo rate now stands at 5.75 per cent against 6 per cent earlier.
Acharya will be now returning to the New York University's Stern School of Business in August instead of February 2020.
The market was at 39,120, down 72.10 points as of 10.17 a.m. on Monday.
With Acharya's resignation, the RBI is now left with three Deputy Governors N.S. Vishwanathan, B.P. Kanungo and M.K. Jain.
( With inputs from IANS )