Adebayor is embroiled in a dispute with the Togolese federation over match bonuses and will not represent the national team, according to a spokesman for the player quoted on South African website supersport.com.
Adebayor's public relations officer Amedodji Blaise told the site: "Togo international and captain Emmanuel Adebayor hereby brings to the notice of the general public that he is suspending his international career with the Togo team.
"The atmosphere currently prevailing within the Hawks will not help the team achieve its set-out objectives."
The Nations Cup is taking place in South Africa and runs from January 19 until the final on February 10.
Adebayor last week criticised his national federation for failing to pay bonuses following a 1-0 friendly win over Morocco.
The 28-year-old former Manchester City striker had retired from international football in early 2010 following an armed attack on the Togo team bus in Angola but he made a return to the team earlier this year.