Ancient Egyptian hieroglyphics were not deciphered in the modern era until 1822 (through the agency of the Rosetta stone), so while superstitions regarding mummies and disturbed burials may have existed before that point, the "mummy's curse" was not. Execration texts and curses on Egyptian tombs were themselves relatively rare, although they became a feature in Egyptology accounts. Zahi Hawass records one such:

All people who enter this tomb,

Who will make evil against this tomb and destroy it:

May the crocodile be against them in water,

And snakes against them on land.

May the hippopotamus be against them in water,

The scorpion against them on land

• The Golden King: The Legend of Tutankhamun 148

Mummies weren't unknown in Europe and were mentioned in some fiction; Mary Shelley's Frankenstein, or, The Modern Prometheus (1818) includes the line:

Oh! No mortal could support the horror of that countenance. A mummy again endued with animation could not be so hideous as that wretch.

Likewise, Roger Luckhurst in The Mummy's Curse: The true history of a dark fantasy recalls a line from Thomas de Quincy's Confessions of an English Opium Eater (1821):

I came suddenly upon Isis and Osiris: I had done a deed, they said, which the ibis and the crocodile trembled at. I was buried for a thousand years in stone coffins, with mummies and sphynxes, in narrow chambers at the heart of eternal pyramids. I was kissed, with cancerous kisses, by crocodiles; and laid, confounded with all unutterable slimy things, amongst reeds and Nilotic mud.

So the idea of mummies being a part of a dark supernatural milieu and the reanimation of the mummy was already present. Post-1822, the mummy fiction properly began with Jane Loudon Webb's The Mummy! A Tale of the Twenty-Second Century (1827), which involves the revived mummy of Cheops. This was followed by "La Pied de momie" (1840) ("The Mummy's Foot" translated into English by Lafcadio Hearn in 1863). The first short story featuring mummies in English was Edgar Allan Poe's "Some Words with a Mummy" (1845) - which featured galvanism and reanimation.

The first tale which really had an element of revenge to it i the anonymous "The Mummy's Soul" (1862), published in The Knickerbocker magazine, and while it does not explicitly mention a curse, the act of supernatural revenge for the desecration and theft from a mummy's tomb is very familiar. Louisa May Alcott's "Lost in a Pyramid; or, The Mummy's Curse" (1869) may be the first story to really bring all these elements together, although it follows a lot of the general themes of earlier fiction:

"Among his spoils, Niles found a bit of parchment, which he deciphered, and this inscription said that the mummy we had so ungallantly burned was that of a famous sorceress who bequeathed her curse to whoever should disturb her rest. Of course I don't believe that curse has anything to do with it, but it's a fact that Niles never prospered from that day. He says it's because he has never recovered from the fall and fright and I dare say it is so; but I sometimes wonder if I am to share the curse, for I've a vein of superstition in me, and that poor little mummy haunts my dreams still."

This Gothic turn to the Egyptian theme reflected a less-rosy reception of things Egyptian in the 1860s on, reflecting the difficulties of colonial administration and trade conflict with the American South, rumors of mummy paper, etc. (Luckhurst 166) With the British occupation of Egypt in 1881, post-occupation tales emphasized curses and revenge, especially:

Guy Boothby's Pharos the Egyptian (1899), Sax Rohmer's Tales of Secret Egypt (1918), Richard Marsh's The Beetle (1899), and Bram Stoker's The Jewel of the Seven Stars (1903).

I might add H. Rider Haggard's She (1886), Arthur Conan Doyl's "The Ring of Thoth" (1890) and "Lot No. 249" (1892), Algernon Blackwood's "The Nemesis of Fire" (1908), and Sax Rohmer's Brood of the Witch Queen (1914) as all being very influential in the genre as well.

Much more mummy-fiction followed as Europe fell into Egyptomania in the late 19th/early 20th century, and "The Curse of the Pharaohs" was spread wide by the 1922 discovery of the tomb of Tutankhamun, the 1922 epic The Ten Commandments, and the 1932 Universal horror film The Mummy starring Boris Karloff.