The west African country, which claimed the Cup of Nations trophy in 2017 in Gabon, was deemed to be too far behind with its building programme. There were also fears about security following attacks from insurgency groups.
"The Egyptian football federation declares its candidacy to host the 2019 African Nations Cup," it said in a statement on Twitter and Facebook.
South Africa confirmed its candidature on Thursday night. "We have submitted our bid documents," South African Football Association spokesman Dominic Chimhavi told AFP. "It is now up to Caf to decide who hosts the 2019 Cup of Nations."
The decision as to who will replace Cameroon will be made in Senegal on 9 January.
If South Africa were to be chosen, it will be third time it has replaced another country as hosts of a tournament first staged in Sudan 61 years ago.
It took over from Kenya in 1996, going on to win the competition. Violence following the downfall of Moamer Kadhafi prevented Libya from organising the 2013 edition and South Africa stepped in three years after becoming the first African country to stage the World Cup.
Egypt, which has won the Africa Cup of Nations a record seven times, last hosted the event in 2006. They beat Cote D'Ivoire in the final in Cairo.
Then it was a 16 team affair. The 2019 Cup of Nations will be the first to feature 24 sides. It will also be the first to take place in June and July rather than January and February.