The two plaster-covered wooden lids had been sawed in two, causing irreparable damage. The covers were adorned with decorations and ancient Egyptian hieroglyphics.
The authority says one dates between the 16th and 14th centuries BC and the other to between the 10th and 8th centuries BC.
Egypt officially demanded Israel to return the artifacts on Tuesday, local media reported.
According to the reports, Egypt's Antiquities Ministry have requested the police and the country's Interpol branch to help recover the objects.
In a statement, released Tuesday, the Israel Antiquities Authority said that robbers had likely plundered Egyptian tombs and smuggled the covers to Dubai. From there, the lids made it to Israel through Europe.
It was not known when the items were stolen. The IAA said Israel is examining how to return the covers to Egypt.
According to the IAA, up until recently antique dealers have abused loopholes to import stolen artifacts from across the Middle East to Israel, where documents were forged to allow these items to be exported to Europe.
On April 20, a new legislation will go into effect, allowing the authority to put a stop to the illegal antique trade, IAA official Shai Bar-Tura said.
Roi Kais contributed to the report