Abdul Hye, the chief of the ruling party's Narayanganj district unit, called journalists to his home on Saturday to issue the warning.
"A board headed by Prime Minister Sheikh Hasina has nominated Ivy. Our reaction is only this - whoever gets the 'boat' symbol is our candidate," Hye said.
Congratulating Ivy on winning the nomination, he said, "I believe the leaders and activists of our party and its affiliates will work for the party."
"But if someone works against the party candidate secretly, he or she will have to face organisational action," he added.
Ivy wants Anwar to lead her campaign again
Ivy became mayor by defeating another leader of the party AKM Shamim Osman in the first polls to the NCC five years ago.
Their feud came out in the open to make headlines many times. They also traded ugly comments at a live TV talk-show.
Awami League on Friday nominated incumbent Mayor Ivy to seek re-election in the Dec 22 polls, snubbing its city unit recommendation that Anwar to be the candidate in the polls.
Anwar was the chief coordinator of Ivy's campaign during the 2011 polls.
Ivy on Saturday said she wants Anwar, whom she termed 'a real Awami Leaguer', to lead her campaign again.
"I respect him very much. She was in charge of my campaign earlier. I want him to do the same again," she told reporters at her home.
She said it was 'natural' for a 'large' party like Awami League to have difference of opinion or internal feuds.
"But when the party makes a decision, everyone follows it," she added.