The Desert Foxes claimed that they were attacked by a group of Egyptian hooligans shortly after landing in the Egyptian capital to play a crucial World Cup qualifier last November.
The Algerians supported their claims with a video showing that Rafik Halliche and Khaled Lemmouchia, among others, suffered head injuries in the attack.
A hearing was held early on Tuesday, where Egyptian FA officials were summoned to explain the allaged attack on Algeria's bus.
A decision from the world football governing body was made several hours later.
Apart from relocating two World Cup qualifiers, FIFA fined Egypt CHE 100,000 (around EGP 500,000).
A punishment on the Pharaohs was widely expected as the host nation is responsible for the safety of visiting team.
Over the past few months, there were fears that FIFA would deduct points from the African champions in the upcoming World Cup qualifying stage.