The killings are thought to have taken place last year on a ranch in the western state of Michoacan last year.
President Enrique Pena Nieto said he had dismissed Mr Galindo to allow for a transparent investigation.
Earlier this month Mexico's National Human Rights Commission accused police of tampering with evidence.
Michoacan: Mexico's failed state?
One police officer and 42 suspects were killed in the raid on a ranch in Tanhuato in May last year.
Officers said they had returned fire in self-defence but the high death toll aroused suspicions.
The human rights commission report accused police of planting guns on some suspects and moving bodies to bolster the official version that all the deaths occurred during a gun battle.
Mr Galindo and National Security Commissioner Renato Sales have denied anyone was summarily killed and insisted officers used necessary force against highly armed criminals.
Police used a Black Hawk helicopter during the operation, reportedly firing some 4,000 rounds into the ranch, known as the Rancho del Sol, during the initial assault.
The helicopter itself was hit by gunfire, investigators found.
In its report (in Spanish; warning: contains graphic images), the CNDH asserts that:
Michoacan has become one of Mexico's most violent states because of the rivalry between cartels.
Mexico's federal police chief, Enrique Galindo, has been sacked following allegations police killed at least 22 suspected members of a drugs cartel.