Namibia, beaten twice by Burkina Faso in the qualifiers, alleged that their opponents had fielded Cameroon-born defender Herve Zengue when he was not qualified to play.
However, on Tuesday the Lausanne-based Court of Arbitration for Sport (CAS) dismissed Namibia's appeal against the African confederation's decision not to sanction Burkina Faso.
The CAS said it was satisfied that Zengue, who plays for Russian-based club Terek Grozny, was eligible to play for the West Africans under FIFA rules.
"Herve Zengue was born in Cameroon and took a residency in Burkina Faso in 1994," it said in a statement.
"He got a Burkinabe nationality certificate on September 14 2006. On March 25 2011, the player received a five-year passport from Burkina Faso."
CAF had initially rejected Namibia's protest on a technicality while Burkina Faso said Zengue was eligible to play for them because he was married to a Burkinabe woman.
The Cup of Nations, being staged in Gabon and Equatorial Guinea, kicks off on January 21.
FIFA statutes say that, in addition to being granted nationality, a naturalised player must have lived in his adopted country for at least five years.
Zengue was not included in Burkina's cup squad named last week.
Burkina have been drawn in Group B with Ivory Coast, Sudan and Angola.
Namibia lost 4-0 away and 4-1 at home to Burkina in qualifying but wanted to be given 3-0 forfeit wins for each game which would have resulted in them finishing top of the group.
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