Northern Territory Sports Minister Nathan Barrett has resigned after being accused of sending a female constituent two sexually explicit videos of himself.

Mr Barrett, who was tipped to become treasurer, reportedly sent the explicit videos via Facebook, according to the NT News.

He issued a statement on Saturday saying he had tendered his resignation to Chief Minister Adam Giles.

Mr Barrett, a married father of three, apologised to his family, constituents and Territorians for "engaging in an inappropriate relationship".