Laith Samaradali, 25, shouted and swore when his brother Jordan Samaradali's fight came to an end at the SECC on July 29.
When a member of the public, Christopher Savage, told Samaradali to watch his language because there was children about, he turned his anger on him.
The Australian threw a bottle at Mr Savage but missed, and hit a seven-year-old child who burst into tears.
Samaradali was arrested and appeared the following day at Glasgow Sheriff Court where he pled guilty to using threatening and abusive behaviour, and assaulting the child to his injury.
He was ordered to pay £200 to Mr Savage and the child - who cannot be named.
Passing sentence Sheriff Norman Ritchie QC told him: "According to some the games aren't quite as good as the Olympics but they are a big event for Glasgow."
He told Samaradali: "You were welcomed here to support your brother as people around the planet were welcomed to this country."
The sheriff branded his behaviour "all too common" and told him he turned his abuse to the member of the public that pointed out the "error of his ways".
He added: "That young boy was attending an event in the city which should have left him with long lasting, pleasant memories. Now, he will have the recollection of a bad man shouting and swearing and throwing a bottle at him."
As Samaradali left the court building with his wife and carrying his baby he said: "Dreams have been broken due to bad refereeing".
His wife told the press waiting outside that the bottle hit the child on the arm and that they were "very apologetic".