The actor — filing under his real name, Nicolas Coppola — cited irreconcilable differences as the reason for the split in a petition filed Monday in Los Angeles Superior Court.
There was no immediate comment from publicists for Presley or Cage.
Presley, 34, was married previously to musician Danny Keough and pop singer Michael Jackson. It was the second marriage for Cage, 38, who divorced actress Patricia Arquette in 2000.
Presley has two children from her marriage to Keough, and Cage has a son from a previous relationship.
The two were married Aug. 10 before family and friends at a resort on Hawaii.
Presley is the only child of Priscilla Presley and singer Elvis Presley. Cage won a best-actor Academy Award for 1995's "Leaving Las Vegas." His other recent movies include "Captain Corelli's Mandolin," "The Family Man" and "Gone in 60 Seconds."