Egypt's Supreme Council of Antiquities said it formally requested the return of the piece, known as the mask of Ka Nefer Nefer, which the museum says dates back to the 19th Dynasty, 1307-1196 BCE.
"The mask is in a very well preserved condition and it features the bust of a young lady called Ka Nefer Nefer... It has a combination of glass inlaid eyes, a face covered with gold and a wig," Zahi Hawass, Egypt's antiquities chief, said in the statement.
The council said the piece was discovered in 1952 in the unfinished step pyramid at Saqqara, outside Cairo. It was stored at the site until 1959, when it was taken to the Egyptian Museum.
But due to poor storage and the primitive documentation system used at the museum at the time, the mask disappeared and it was believed to have been smuggled out of the country.
The St. Louis Art Museum, in the US state of Missouri, purchased the piece in 1998.
Jennifer Stoffeo, a spokesperson for the museum, said they had received the Egyptian request. "We have written back asking for more information and included our research. We would like to come to a solution because we don't think that it was obtained illegally or improperly."
The SCA said it also asked Basel Museum in Switzerland to return the left eye of a statue of king Amenhotep III, which it said was stolen from a temple in Luxor several years ago.