Dwyer, 25, was arrested by Phoenix police after two alleged incidents in July, with the Cardinals moving quickly to bench him.
In a statement, the Cardinals said: "We became aware of these allegations this afternoon when notified by Phoenix police and are cooperating fully.
"Given the serious nature of the allegations we have taken the immediate step to deactivate Jonathan from all team activities.
"We will continue to closely monitor this as it develops and evaluate additional information as it becomes available."
Dwyer was arrested on charges of one count of aggravated assault causing a fracture, one count aggravated assault involving a minor, two counts of criminal damage and one count of preventing the use of a phone in an emergency, and assault.
Police said Dwyer had admitted to the incidents, but denied any physical assaults.
It continues a tumultuous week for the NFL as it deals with domestic violence incidents involving former Baltimore Ravens running back Ray Rice and Carolina Panthers defensive end Greg Hardy.