Abercrombie said Gabbard should step down and allow a special election to fill her seat.
Gabbard, who has served in the House since 2013, has already said that she will not seek reelection to focus on her presidential campaign.
Abercrombie served as Hawaii's governor from 2010 to 2014.
According to GovTrack, Gabbard has missed about 86 percent of House votes in the last three months.
“Hawaiʻi is Congresswoman Tulsi Gabbard’s home and her heart,” communications director T. Ilihia Gionson said in a statement.
Gabbard is considered a long shot to win the Democratic presidential nomination and did not qualify for last week's debate.
"I could not in good conscience vote against impeachment because I believe President Trump is guilty of wrongdoing," Gabbard said in a lengthy statement last week. »