The auction will be conducted on BSE's ebidxchange platform from 1530 hours to 1730 hours after the close of market hours, the exchange said in a circular.
The debt auction quota gives overseas investors the right to invest in the debt, up to the limit purchased.
A mock bidding session was conducted today to check the system's performance.
"Live bidding session for allocation of debt investment limits for FII/FPI and sub-accounts shall be conducted on June 15, 2017 on the exchange's ebidxchange platform," BSE said.
To boost inflows of foreign funds into Indian capital markets, regulator Sebi in April raised the FPI investment limit in central government securities to Rs 1.85 lakh crore from Rs 1.52 lakh crore.