Brazil passed a law in 2003 which banned the sale of alcohol in stadiums in a bid to halt spectator violence.
The ban has been eased for the World Cup, from June 12 to July 13, with some observers saying this was demanded by FIFA to save a sponsorship deal with Budweiser, the beer brand owned by AB InBev.
Gassmann called for "a change of mentality" by FIFA. "Economic interests must not prevail over the health and security of spectators," he told a Berlin press conference.
"We demand that FIFA respect the law of a democratic country like Brazil," he added.
Brazilian brewers expect a major sales boom during the World Cup.