SÃO PAULO—The secretary-general of FIFA, Jérôme Valcke, has expressed concerns about levels of drunkenness at World Cup matches, and suggested the organization may need to ban some sales of beer.

"I was amazed by the number of people who have been drunk, by the level of alcohol people had," Valcke said in an interview with Brazil's SportTV channel. "I don't know why I don't think it's just a specific thing to this World Cup but I was a bit surprised by the level of alcohol which was taken by people, and maybe...