The cousin of the boy named Abbas, who taped the video which was posted online overnight Friday, was also arrested, the National News Agency said, quoting a police statement.
It identified the victim as a nine-year-old boy from Syria named Khaled.
In the footage posted by Ya Sour website, Abbas swings a club at Khaled, beating him on various parts of his body, slapping him and kicking him, as adults who are heard but not seen urge him on.
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Justice Minister Ashraf Rifi ordered an investigation and late on Saturday police arrested "Abbas's father and his cousin who taped the video after a probe involving online activists," the news agency said.
The video caused outrage across Lebanon with angry comments posted on Facebook and Twitter, and one user saying she was "ashamed of being Lebanese".
In the video, Abbas clutches a club with his pudgy hands, hitting the other boy, punching him in the face, slapping him and kicking him in the shin.
Adults and children offscreen demand a tougher beating and order the boy, who tries repeatedly to shield himself with his arms, to stay still.
"Abbas hit him, don't be afraid," a male voice says.
Abbas, who has a pony tail and fine features like a girl, is told to slap the boy and does so, then is told to kick him in the stomach and again complies as if it is a game.
The victim whimpers, gets on his knees, implores God and tries again to shield himself.
Another voice, seemingly a young boy, is heard saying: "That wasn't too hard," referring to the blows.
The male adult comments: "No it isn't strong" and urges Abbas to give the other child "a boxing". "Yalla Abbas," he says using an Arabic word that means 'go on'.
"When I saw this shameful video I felt, for the first time, ashamed of being Lebanese," said one Facebook user.
Another commentator accused the parents of Abbas of "raising the child to be a racist from his early age."
Lebanon hosts more than a million refugees from Syria's civil war and Rifi told AFP the boy was probably Syrian from the eastern Bekaa Valley where many Syrians have found refuge.
