Both sides are eliminated from the race for the third and final qualifying round after they failed to win their last game.
Zimbabwe went down 1-0 to South Africa, courtesy of a first-half strike from Teboho Mokoena for the hosts.
Ethiopia, meanwhile, denied Ghana with a second-half equalizer, Getaneh Kebede scoring in the 76th minute to cancel out Andre Ayew's opener for the visitors.
However, it wasn't enough to keep their progression hopes alive, with the side left trailing leaders South Africa by nine points.
Zimbabwe are at the bottom with just one point, having drawn to South Africa on the opening matchday.
They're one of only nine sides still winless in the second round of these qualifiers after five games in the CAF zone.
Zimbabwe vs Ethiopia Head-To-Head
Ethiopia have won three of their previous four clashes with Zimbabwe, losing once.
The reverse fixture between the sides in September also ended in a 1-0 victory for them.
Aschalew Tamene scored a penalty in the 94th minute to break Zimbabwean hearts.
Zimbabwe Form Guide (all competitions): D-L-L-L-L
Ethiopia Form Guide (all competitions): L-W-L-L-D
Zimbabwe vs Ethiopia Team News
There are no injury concerns for the Warriors at the moment.
They've failed to score in their last two games and will be hoping to break the duck here.
Getaneh Kabede has scored twice in Ethiopia's last three games and will be hungry to add more to his tally.
The upcoming clash will also be his 60th for the Walia ibex, with only Shimelis Bekele playing more (66).
Zimbabwe vs Ethiopia Prediction XI
Zimbabwe (4-3-3): Petros Mhari; Bruce Kangwa, Brendan Galloway, Kelvin Madzongwe, Takudzwa Chimwemwe; Marvelous Nakamba, Gerald Takwara, Ishmael Wadi; Khama Billiat, David Moyo, Blessing Sarupinda.
Ethiopia (4-3-3): Teklemariam Shanko; Asrat Tunjo, Aschalew Tamene, Mignot Debebe, Ramadan Yesuf; Shimelis Bekele, Mesud Mohammed, Amanuel Yohannes; Dawa Hotessa, Getaneh Kebede, Abubeker Nassif.
Zimbabwe vs Ethiopia Prediction
With both teams already eliminated from the race for the third qualifying round, they won't be too motivated to play to the best of their ability.
That could see them play out a low-scoring stalemate.
Prediction: Zimbabwe 1-1 Ethiopia
Where does Mane rank in Paul Merson's 5 greatest Liverpool signings of the Klopp era? Click here