The Senate voted 43-7 in favour of Senate Bill 154, which will now go to the House.
North Carolina law already allows the Eastern Band to offer live poker, slot machines and video-style games.
Eastern Band Principal Chief Richard Sneed said in an interview sports wagering would provide new amenities to patrons.
The state also said it would see a slight increase in revenue as a direct result of the decision.
Republican Senator Jim Davis, who filed the bill, said: "It is expected it will enhance the revenue of the tribe [by] about $14 million a year and that will yield about $1 million for the state."
States such as Delaware and Rhode Island have fallen well short of sports wagering revenue projections in recent months, while the state of New Jersey has thrived since legalising sports betting.
Two tribal casinos currently offer sports betting in New Mexico, although they did not require Senate approval due a binding compact with the state.
