Cardy had announced he would resign as leader after the NDP did not win any seats in last month's provincial election.
The move follows an effort by party members to convince him to enter the race.
Acadian lawyer Joyce Richardson announced her intention last week to seek the NDP leadership and nomination for Saint John East, but says she recently learned she isn't eligible to run in the byelection.
Richardson says she doesn't meet the requirement that potential candidates be members of the party in good standing for two weeks before a nomination meeting is held.
The Greens have chosen Sharon Murphy, who was their party's candidate in the Sept. 22 election, to run in the byelection.
Saint John Deputy Mayor Shelley Rinehart is running for the Liberals while Glen Savoie, who lost the election in that riding by nine votes, will represent the Opposition Progressive Conservatives.
The seat became vacant last week after Liberal Gary Keating quit politics, saying the hours and travel that come with the job would have a negative impact on his health and family.
The byelection is Nov. 17.