The answer to this question varies, depending on who you talk to and how “novel” is defined. If a novel is treated as a prose narrative of significant length, the oldest novel is probably The Tale of Genji, written by Murasaki Shikibu in 11th century Japan. The Tale of Genji is certainly recognizable as a novel to modern eyes; in fact, it continues to be widely read, and it has been translated into numerous languages. This book had a tremendous influence on Japanese literature, and it continues to be cited as a major source of inspiration by prominent Japanese novelists today.
However, when one includes epic poems under the field of “novel,” and some scholars do, matters get a bit more complicated. Both The Epic of Gilgamesh and The Odyssey are far older than The Tale of Genji, and they could in a way be considered precursors to the modern novel. The Odyssey in particular has had an immense influence on Western culture and literature; themes from this epic poem pop up again and again in Western art, music, and writing. If you don't consider The Odyssey the oldest novel since it doesn't meet the strict definition of a novel, it was most certainly influential.
The dispute over the identity of the oldest novel might seem petty, but it can be intriguing and quite revealing. People who support publications like Robinson Crusoe (1719) as “the first novel” are choosing to blatantly ignore works like The Tale of Genji, along with numerous so-called “Romances” written in Spanish, French, and Italian as early as the 12th century. Robinson Crusoe is also hardly the oldest novel in English, although modern readers might have trouble understanding the English used by authors like Geoffrey Chaucer.
In the West, the form of the novel appears to have emerged around the 15th century, although several outliers were written earlier. Books like Le Morte D'Artur, The Canterbury Tales, and The Adventures of Esplandian were all published in the 1400s, paving the way for publications of huge numbers of novels with the advent of the printing press and movable type. The word “novel” itself entered the English language around 1566, right on time for Miguel de Cervantes to write La Galatea and later Don Quixote. The word is derived from the Italian novella. By the 16th century, the novel was a firmly entrenched literary device, and it shows no signs of abating today.
One of the most remarkable things about the novel is that this form is incredibly enduring, despite, or perhaps because of, its simplicity. Historical evidence also seems to suggest that various forms of the novel evolved independently, which is part of the problem with deciding on the true “oldest novel.” Apparently something about this simple but incredibly flexible form of literary expression just works for authors around the world.