This will be the first meeting between the two nations in a competitive tournament.
Both teams have previously hosted the Africa Cup of Nations. The Walya Antelopes staged the event in 1962 while the Stallions hosted the competition 36 years later.
Burkina Faso is considered the weakest of the eight west African nations at the 2013 Afcon, despite gracing the tournament in eight of the last nine occasions.
Ethiopia is the lowest ranked team at the 2013 Afcon as they are positioned at 110, while Burundi is placed 92nd.
The Walya Antelopes are making a return to the competition after a 31-year absence.
Paul Put took over from Portuguese manager Paulo Duarte in March following the Stallions' woeful return from the 2012 Nations Cup, where they lost all three of their games and crashed out in the group stage.
Captain Moumouni Dagano (pictured right), who joined the national team in 1999 while playing for local side Etoile Filante, remains Burkina Faso's all time top scorer with 31 goals.
Ethiopia will face Burkina Faso without the services of goalkeeper Jemal Tessaw, who was red, carded for a professional foul during the opening match against defending champions Zambia.