They had been due to face South Sudan in the first round of the preliminary phase over two legs in April.
South Sudan, entering the competition for the first time, will now go though to the preliminary phase second round.
No reason has been given for Eritrea’s withdrawal, but recent defections by players may have led to the decision.
Seventeen players from the Eritrean squad, plus the team doctor, absconded at the 2012 East and Central Africa Senior Challenge Cup in Uganda.
In 2011, 13 Eritrean players sought asylum in Tanzania after the same tournament, while 12 members of the Eritrea squad disappeared and sought asylum in Kenya during the regional tournament in 2009.
Four Eritrean athletes also left their base and sought political asylum in Britain after the London Olympics in 2012.
Between 2,000 and 3,000 Eritreans flee the small east African country every month, a United Nations report said last year.
South Sudan will find out who they will play in the second round when the draw is made on Sunday, 27 April in Cairo.