The two players have been major doubts for the fixture since pulling out of training on Wednesday over injury concerns.
Coach James Kwesi Appiah had hoped for a quick recovery as he seeks to end the disappointing qualifying campaign on a high.
"Tests have revealed that Ghana captain Asamoah Gyan won't play in Sunday's World Cup qualifier against Egypt," the GFA announced via their official Twitter account.
"Team doctor says scans show Gyan suffered at thigh strain following his injury in Black Stars training two days ago."
It becomes the fourth successive time the former Sunderland frontman is forced out of a Ghana match after sitting out the last three games against Congo, Uganda and Saudi Arabia.
Newcastle United star Atsu, on the other hand, has failed to recover from a thigh injury picked up while in club action.
"Tests have revealed that winger Christian Atsu will not play for Ghana in Sunday's World Cup qualifier against Egypt," the GFA has revealed.
"Team doctor says the scans show Atsu suffered a thigh muscle tear."
While playing against Bournemouth in the English Premier League on Saturday, Atsu tweaked a muscle after attempting a shot, leading to his withdrawal moments later.
Despite the injury concern, the former Porto star reported for international duty, but a relapse while training with the Black Stars has ended his hopes of playing against the Pharaohs on Sunday.
The 25-year-old also missed last month's games against Uganda and Saudi Arabia due to injury.
Astana winger Patrick Twumasi is also a doubt for the Sunday after picking up an injury during the Black Stars' friendly against local academy side Glow Lamp on Thursday.