Charlie Chan has been hired by a French scientific organization to investigate sales to the collectors market of artifacts from a tomb whose excavations they had funded, and in the course of things he discovers that the body of a murdered archaeologist has been concealed as an ancient mummy. (An X-ray reveals that the mummy had died from a gunshot, which naturally arouses his suspicions.)
The film is painfully dumb, with none of the witty dialog seen in better films of the series. Stepin Fetchit is around for alleged comic relief in a role that isn’t just a cringe-provoking racial stereotype but even has him speak of having been “won” at gambling by one of the supposed good guys, who thinks nothing of striking Fetchit for moving too slowly for him. It's really painful to watch.
(Mantan Moreland played a similarly comic role in other Charlie Chan films but was for my tastes nowhere remotely as offensive, and in fact created some of the comic bits in them himself. For examples, see this earlier post.)
In fairness to Fetchit, real name Lincoln Perry, his "Laziest Man in the World" character was hugely popular with audiences, so much so that he was the first black actor to get starring credit in films and the first to become a millionaire. Very different in real life from his screen roles, he was close friends with Will Rogers and wrote regularly for The Chicago Defender, a major African American weekly newspaper. His Wikipedia article (link) has more on his life and career. And to belabor an obvious point, he can't be blamed for this film's lousy screenplay.
While I can't recommend the film, one of the extras on the DVD is worth seeing: a short documentary about an early-20th-century Hawaiian police detective named Chang Apana (1871-1933). Detective Chang was not well educated, but he was fearless, incorruptible, and much admired. At one point he single-handedly arrested 70 people in a gambling den using nothing but the force of his authority and reputation. Like Indiana Jones, his favored weapon was a whip, and he was called on to demonstrate tricks with it on numerous occasions. Chang was sometimes said to have been the inspiration for Charlie Chan, and in later years people even took to calling him Charlie Chan, but he had little in common with the character besides being a Hawaiian detective of Chinese ancestry. For more about him see his Wikipedia article (link), which says that Chang enjoyed the Charlie Chan films and met Warner Oland, the Swedish American actor who played Chan in 16 of the movies, during the filming of The Black Camel on location in Hawaii.
Charlie Chan's creator, Earl Derr Biggers, reportedly read about Chang while vacationing in Honolulu in 1919, and this might have given him the basic idea for the character. But Chang and Chan did not much resemble each other in physique or personality. According to Bigger's wife, Chan’s physical description in the novels was pretty close to that of the author himself, not the cop. Incidentally, Charlie Chan spoke standard English in the books. The exaggerated accent was an invention of the movies. Pretty much the same thing happened to Tarzan.
I wasn't able to find a trailer for Charlie Chan in Egypt, but you can find the whole film on YouTube if you want to see if it's as bad as I've described. To be fair, not everyone agrees with my low opinion.
(Updated 2016 September 12 to correct a typo and clarify some wording in a couple of places.)