Mohammed Kudus scored both goals for Ghana soon after Salah went off in the Group B clash at the Felix Houphouet Boigny Stadium.
Omar Marmoush pounced on an error to equalise for Egypt midway through the second half, but Kudus struck again right away to restore Ghana’s lead.
The Black Stars made another mistake as Mostafa Mohamed levelled on 74 minutes, leaving Ghana with just one point from two matches.
Ghana have now won just one of their last 11 AFCON matches. They were stunned 2-1 in their first game by Cape Verde, the smallest nation in the tournament who can clinch a last-16 place and top spot in the group with victory over Mozambique on Friday.
Both sides went into the Group B match in need of a positive result, after Egypt opened their AFCON campaign with a draw against Mozambique and Ghana were beaten by Cape Verde.
Should Cape Verde beat Mozambique on Friday, they will be through to the knockout stages as group winners.
The Black Stars must win their final group-stage match against Mozambique if they are to avoid a second-straight group-stage exit, while Egypt also has to win their final group-stage match against Cape Verde.
The biggest concern for Egypt is Mohamed Salah’s injury, who came off after picking up a first-half injury, just before Mohamed Kudus opened the scoring.
Salah looked emotional as he left the pitch but no diagnosis has been carried out.
Liverpool will be hoping that the problem is minor with Jurgen Klopp reliant on the striker this season.