Enyimba of Nigeria, who lost 1-0 at home to Wydad Athletic Club of Morocco in the first leg, were unable to fly to Casablanca on Monday night as planned because Moroccan authorities did not grant them a landing permit for their chartered aircraft.
The match, which was scheduled for Wednesday, will now take place on Thursday at 10pm Cairo time, CAF said in a statement.
Moroccan media reported that a storm was hitting the coastal, northern, and eastern cities of the country with wind speeds reaching 100 kilometres per hour, but CAF did not mention this as a reason for the postponement.
Wydad are favourites to advance to the semifinals of the inaugural edition of the competition after Yahya Jabrane scored a penalty in the first leg in Uyo on Sunday night.
CAF also moved the quarterfinal second leg in Tunis between Esperance of Tunisia and TP Mazembe of Congo Democratic Republic from Wednesday to Thursday.
No official explanation was provided for the decision.
The first leg in Kinshasa ended in a 1-0 win for Mazembe thanks to a header by Cheick Fofana in the first half.
The winners of the two matches will meet in the semifinals, which are scheduled for 5 and 12 November. The final will be played over two legs on 26 November and 3 December.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)