The former minister for sports, young Territorians and assistant treasurer, resigned from the ministry on Saturday after the reports emerged.
CLP president Tory Mencshelyi confirmed Mr Barrett would not contest the poll, which is due to be held on August 27.
“This has obviously been a decision that’s come about after what has been in the paper,” Ms Mencshelyi said.
She said Mr Barrett decided to quit due to family interests as well as pressure from the party, with some believing his candidacy was untenable.
“I don’t tolerate this sort of behaviour,” Ms Mencshelyi said.
“The party will not tolerate this type of behaviour.”
She said the CLP would now start a process to select a new candidate, hinting that a female candidate would be welcomed.
Labor leader Michael Gunner said the decision was “the right decision,” but added that Mr Barrett should be booted from the party.
Barrett ‘would have found it tough to campaign’
ABC election analyst Antony Green said Mr Barrett would have found it difficult to campaign in the election.
“He can’t go out and campaign face-to-face, which is such an important part of campaigning in the Northern Territory,” Mr Green said.
“The electorates are only 5,000 people. You’ve got to go out and talk to your constituents to get re-elected.”
Mr Barrett entered Parliament in 2014, winning the seat of Blain after the former CLP chief minister Terry Mills resigned from Parliament.
The seat, situated in Palmerston, is considered a safe Country Liberals seat with Mr Barrett winning 53.2 per cent of the two-party preferred vote despite a swing against the party.
“The CLP’s got a difficult task of trying to win the next election, they’re clearly suffering from huge amount of internal disruption,” Mr Green said.
“Only once has Labor broken into Palmerston and that was when Claire Martin took Labor to a landslide re-election in 2005.”
Implications for federal election
Another concern for the CLP is whether this latest scandal will impact on the chances of re-election for Natasha Griggs, who holds the federal marginal seat of Solomon that encompasses Darwin and Palmerston.
“For the Turnbull Government to be re-elected they need to hold seats like Solomon,” Mr Green said.
“Labor already had a good chance because of the unpopularity of the Territory Government.
“To have this scandal blow up three-weeks before the election just adds to that public ridicule.”
On Saturday Ms Griggs told the ABC Mr Barrett should “reconsider his future” in politics, after condemning his behaviour as “very disappointing”.