The 28-year-old, who was videoed while in his native Ivory Coast, apologised after pictures of him were published in a national newspaper.
The Premier League club said the player's action were not "appropriate" and he had been "reminded" of his role model responsibilities.
Tiote said: "I deeply regret my actions and I am sorry for any offence caused."
He added: "I realise that as a professional footballer, I have a responsibility to many people, including the club and its supporters and it is important for me to set a good example to others with my behaviour on and off the pitch."
A statement from the club said: "Newcastle United has been made aware of a video of Cheick Tiote driving while holding a bottle of alcohol, which is understood to have been filmed in Abidjan, Ivory Coast.
"Clearly his actions were not appropriate. The club have spoken privately with Cheick and reminded him of his significant responsibilities as a representative of Newcastle United and a role model."
The player signed a new six-and-a-half-year deal at Newcastle in February 2011.
Newcastle United midfielder Cheick Tiote has been filmed driving while holding an open bottle of champagne.