Fincher was the third filmmaker who decided to pass on the project, which has been in development since 2010, reported Aceshowbiz.
In October last year, "Titanic" helmer James Cameron was attached to the gig, but he let it go due to his commitment to the "Avatar" film franchise. Later "The Bourne Ultimatum" director Paul Greengrass was tapped in but he also bailed out of the project due to unknown reasons.
Fincher's decision to quit the "Cleopatra" movie is surprising since he recently expressed his enthusiasm for the project.
"That's something I would love to do with Angie. It's something that was brought to me that you have to take seriously," Fincher had said.
The film is an adaptation of Stacy Schiff's book "Cleopatra: A Life". The story sees Cleopatra as a firm ruler and military tactician who embarked on a ruthless rise to power. She twice married her brothers, killing each of them as well as a sister.
Romantic alliances with the much-older Roman honchos Julius Caesar and Marc Antony helped her solidify power, but her dalliance with Antony undid both of them.
