The move has been reported as a way to pressure Prime Minister Tony Abbott into deciding on whether his MPs will be allowed a conscience vote.
The draft legislation is almost the same as the private members bill then-MP Stephen Jones proposed to the last parliament, but was defeated in 2012.
Plibersek said she would seek to introduce the bill early this year but it will be up to the Coalition Government to bring on any parliamentary debate.
“Marriage equality’s time has well and truly come,” she said in a statement.
“The proposal for this bill follows the High Court’s confirmation that ‘marriage’ in the Australian Constitution includes a marriage between persons of the same sex.”
Plibersek wanted a Liberal MP to co-sponsor the bill if they were granted a conscience vote.
Abbott opposes any change to the federal Marriage Act but has left open the prospect of allowing his MPs a free vote pending a partyroom debate.
The Greens stated they would support Plibersek’s bill but warned Labor against “rushing” it.