The pair are throwing rival parties for Academy Awards guests, just two miles away from each other, the Daily Mail reports.
Sir Elton's party is taking place at the Pacific Design Centre in Los Angeles. Tickets for the event cost $3,500 (£2,200), which will go towards the Elton John Aids Foundation charity.
Guests due to attend the charity dinner include Katy Perry, Dita Von Teese, Jessica Alba, Heidi Klum and Chace Crawford.
Madonna's event will be held in manager Guy Oseary's home, where Britney Spears, Natalie Portman, Sean Penn, Angelina Jolie, Brad Pitt, Tom Cruise and Jennifer Lopez have all been confirmed to be in attendance. The 53-year-old singer has also scheduled a live performance of her new material.
A source close to Madonna says that she has been personally calling celebrities like Bradley Cooper and Penelope Cruz and inviting them to come.
They said: "'[She] wants to make sure she has better guests than Elton. The war between them has now become quite personal. Most of the big names will go to the Vanity Fair party, then they will head to Madonna's after that."
Madonna and Elton John have been feuding since John accused the singer of lip-syncing during her live tour several years ago.
The 'Give Me All Your Luvin' singer recently performed at the Super Bowl, a performance which John again said she would not sing live in.
Madonna also came under criticism from John's partner David Furnish, after he slammed her Golden Globes win for 'Best Original Song'.
Watch the trailer for Madonna's film W.E.below: