There have been calls on social media for the arrest of the men after the footage emerged this week on the Internet, and their detention is a rare victory for animal rights campaigners who say authorities often ignore such abuses.
The prosecution has remanded the men into custody for four days pending an investigation into charges of killing a domestic animal with no cause, which is banned under Egyptian law, police officials said.
The men later demanded the owner hand over the dog and he did, the police officials added.
They chained it to a street lamp at night and then stabbed and hacked the terrified dog with knives as people watched but failed to intervene, the video showed.
More From This Section
Some onlookers, however, could be heard in the footage pleading for mercy.
Before their arrest, one of the suspects told an Egyptian newspaper that the dog had bitten him "in a sensitive part" of his body days before his wedding and that he had sought revenge.
He later posted a brief video on his Facebook page showing him playing with the dog, named Max.
"I'm sorry Max, I had no choice," he wrote.
Farid al-Deeb, a prominent lawyer and legal expert, told AFP the suspects could face a maximum of six months in prison if they are tried and convicted.