The footage, which is believed to have been taken while the 28-year-old was in his native Ivory Coast, prompted an a statement from the club and an apology from the player.
"I deeply regret my actions and I am sorry for any offence caused," Tioté said.
"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."
Newcastle revealed that they reminded the midfielder or his responsibilities.
"Newcastle United have been made aware of a video of Cheick Tioté driving whilst holding a bottle of alcohol, which is understood to have been filmed in Abidjan, Ivory Coast," their statement read.
"Clearly his actions were not appropriate. The club have spoken privately with Cheick today and reminded him of his significant responsibilities as a representative of Newcastle United and a role model."