Kevin Menicoche said in a statement Wednesday that he plans to address his personal problems and seek professional treatment, but does not specify for what.
The CBC has reported Menicoche and another MLA missed meetings in Inuvik last week because of excessive drinking.
"I feel I may have embarrassed my constituents and deeply regret that," Menicoche, 51, said in his statement.
"I apologize to my constituents for my recent lack of judgement ... I take full responsibility for my behaviour."
He has also asked the legislative assembly to bill him for any extra costs related to the missed meetings.
Tim Mercer, clerk of the legislative assembly, said the government is going to do just that.
"We're not going to charge him for the flights because he did attend certain meetings, but we will charge him for the extra hotel room and the per diem costs."
Mercer said Menicoche attended meetings in Inuvik last Tuesday through Thursday. But he and a another MLA did not attend meetings the following two days with the standing committee on priorities and planning.
Menicoche chairs that committee, said Mercer, who added the meeting went ahead without him.
In his statement, Menicoche said he doesn't plan on leaving his job. He was first elected as the representative for the Nahendeh region 10 years ago.
"I will continue to represent my constituency and carry on the important work of the committees that I sit on."