BJP also decided to field Health Minister Vishwajit Rane from Valpoi constituency. Their names were cleared by the BJP Central Election Committee in New Delhi, a party release said Panaji.
The bypolls will be held on August 23.
BJP's sitting MLA from Panaji Siddharth Kuncolienkar had resigned to make way for 61-year-old Parrikar.
The IIT engineer-turned-politician took over as Goa chief minister in March after resigning as defence minister. The Goa BJP stalwart is currently a Rajya Sabha member and has to get elected to the Assembly to continue as chief minister.
Mr Rane was elected from Valpoi on a Congress ticket in the Assembly polls held in February. Within a few days of declared elected, Mr Rane quit the seat and also the party.
He joined the BJP and was later inducted in the Parrikar-led Cabinet.
He is the son of former Goa chief minister and Congress veteran Pratapsinh Rane.
The main opposition Congress is yet to finalise its nominees for both Panaji and Valpoi seats.