The details of how it broke the rules, or when Bresciano's ban was due to begin, were not immediately clear.
Al Gharafa has said it would appeal FIFA's verdict.
"This is not a unique case, there are many precedents, we as a club are not a part of this case," club's general secretary Jassim Al Manosuri said in a statement on the club's website.
"As the player ended his contract with his former club before joining us, our next step will be filing an appeal to the Court of Arbitration for Sport."
A suspension would jeopardize the 33-year-old's bid to play in a third consecutive World Cup. Australia has qualified for next year's tournament in Brazil. The midfielder has played 72 internationals.