The flight was delayed by half an hour as Saganash was escorted off the plane.
"Neither fatigue nor stress can justify what I did. I need help to overcome a medical problem, a dependence on alcohol, like far too many other Canadians," he said in a statement late Monday afternoon.
"I have asked my leader [Tom Mulcair] to give me leave so that I can take the necessary time to treat this illness. I am deeply grateful for his support and the support of all my colleagues in this difficult period of my life."
A statement from the NDP confirmed that Saganash will be taking sick leave.
Hélène Laverdière will take over Saganash's critic responsibility for international development issues. Charlie Angus and Christine Moore will share responsibility for Saganash’s regional files.
Saganash also apologized to the other passengers on the plane and to the flight crew. He said many of his colleagues can attest to the pitfalls of working in the hectic environment of Parliament Hill.
"I am not looking at excuses, but I know that profound scars were left on me because of my time in residential school. I never shied away from that. The death of my friend and mentor, Jack Layton, also greatly affected me," he said in the statement.
Saganash thanked his constituents and said his office will continue to serve them.
"My priority is to serve my constituents to the best of my abilities and it’s with deep humility that I say thank you and see you soon."
Earlier in the day, Saganash cited stress as the reason he was drinking.
"It was Friday, it had been a long week, and we're all stressed out at that time," Saganash told CBC News on Parliament Hill on Monday. "I apologize."
"This is the first time that it has happened in 30 years in the air. I regret what happened and it won't happen again," he said.
Saganash was elected to represent the northern Quebec riding of Abitibi-Baie-James-Nunavik-Eeyou in 2011. He was a well-known Cree leader and negotiator before entering federal politics.
He ran for the NDP leadership last year but dropped out partway through the campaign. His statement on Monday said the race wore him out and took him away more often from his family than his regular MP duties.