Kuncalienkar tendered his resignation to Speaker Pramod Sawant.
The legislator was first elected from the seat in the by-election held in 2015 when Parrikar was elevated to the Union Cabinet.
He got re-elected from the constituency during the state Assembly elections held in February this year by defeating United Goans' candidate Atanasio Monserratte.
Parrikar, who took oath as chief minister in March after resigning as defence minister, is heading the BJP-led coalition government in his home state.
Parrikar was representing the Panaji seat as chief minister at the time of his elevation as defence minister in November 2014.
Kuncalienkar and another BJP MLA Nilesh Cabral (Curchorem) had earlier volunteered to vacate their seats for Parrikar.