Inspectors reportedly stumbled across the mummy covers while perusing an old Jerusalem marketplace. They confiscated them as suspected stolen property, according to FOX News.
The IAA said the ancient sarcophagus lids were covered with "breathtaking decorations and paintings of ancient Egyptian hieroglyphics" but had been emptied of their contents and sawed in half, damaging them beyond recovery.
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The thieves are suspected of robbing Egyptian tombs and taking the artifacts to Dubai, from Dubai to Europe, and then to Israel, the IAA is reported as saying.
Both artifacts date back thousands of years -- one to somewhere between 16th and 14th centuries BC, the other between the 10th and 8th centuries BC, said AP.
FOX News said mummy-smuggling also has a history that goes back at least to the medieval period, "when Egyptian mummies were ground up into a powder that was thought to have medicinal properties."
It was not immediately clear when the covers were taken or where the mummies that used to be inside them might be.
AP said Israel is discussing how they can be returned to Egypt.