The man's arrest was confirmed by Major General Khalil Al Mansouri, Director of CID, who stressed that the man's actions ran contrary to both the morals of Islam and those of the UAE.
He also warned against further acts of cruelty against animals, stressing that those who break the law will be imprisoned and fined.
According to Article 432 of the emirate's federal law code, a fine of up to AED 1000 ($272) is to be imposed on individuals who neglect and torture a pet in their custody.
The suspect reportedly confessed to the charges against him and was referred to public prosecution.
The video, which was widely shared on social media, showed a man offering the cat in an open cage to two Rottweilers, encouraging them to devour the terrified feline.
"You eat pigeons and chickens?" a man is heard in the video saying to the cat, as it is being mauled by one of the dogs. "Eat the cat, eat it," he orders.
Dr Susan Aylott, a volunteer at Animal Welfare Abu Dhabi, told The National newspaper that this attack was not a rare act of cruelty against animals in the United Arab Emirates.
"We have had several recent incidents like this, including that of a dog whose hind legs were tied and then skinned alive. The abuse has not stopped," she said.