Inglis was also suspended for two tests by the National Rugby League (NRL), ruling him out of matches against New Zealand and Tonga in Auckland this month.
"Greg is not just a great player, he is one of our best role models, but he made a poor decision on this occasion," NRL CEO Todd Greenberg said in a media release.
Only hours after being named captain of Mal Meninga's Kangaroos on Monday, Inglis was stopped by police near the town of Lithgow while driving back to Sydney from a rugby league competition in rural New South Wales state.
He had his licence cancelled and is due to appear in a Lithgow court in November after being charged with "mid-range" drink-driving and speeding offences, state media reported.
Inglis apologised earlier on Tuesday but declined to step down, saying he wanted to see through the process.
"I don't think I let my country down. I think I let a lot of people down where I stand in the game as a proud Indigenous role model, and I think I've let a lot of kids down," he said.
The decision was ultimately taken out of his hands.
"I know I did the wrong thing and, while I am disappointed at missing the tour, I accept the penalty," the 31-year-old said later.
Sydney Roosters skipper Boyd Cordner, who led New South Wales to victory in the annual State of Origin series, is expected to replace Inglis as captain.
The drink-driving charge is another black eye for Australian rugby league and comes two days after the NRL Grand Final ended in controversy surrounding an injury cover-up by the victorious Sydney Roosters.
Roosters staff admitted to lying repeatedly about an injury to halfback Cooper Cronk ahead of the game against Melbourne Storm in a bid to influence their opponents' preparations.
The deceit was slammed on Tuesday by media pundits, who demanded the NRL tighten rules on injury disclosure.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
