Consumer prices rose 7.31% in September from a year earlier, according to the national statistics agency.
This follows a surprise 0.5% interest rate cut at the end of August. The central bank cited a "substantial deterioration" in the global economy in cutting rates to 12%.
Some economists think the bank's action was premature.
"The interest rate cut came too soon," said Oxford Economic's Lloyd Barton.
"It's acting as a trigger for a decline in the exchange rate, and that is exacerbating the central bank's problem with inflation."
However, Brazil's President Dilma Rousseff wants the cost of borrowing to be lowered again. She recently said policymakers must weigh up the threat of a global recession.
The central bank's president, Alexandre Tombini, says he believes the inflation rate will peak in September and then fall back.
The bank targets an inflation rate of 4.5%.
Some analysts think it will have to consider alternative action to prevent one of the big drivers of world growth from overheating.
"They are in a boom phase and face a dilemma," said Professor Ricardo Cabral at Madeira University in Portugal, a former adviser to the World Bank on Brazil.
"Real interest rates were high, causing foreign funds to flow into Brazil, pushing its currency higher. The rate cut may thus have been appropriate.
"To avoid perverse effects on credit growth, the central bank could follow the example of the Chinese and increase bank reserve requirements."
China's central bank has forced its lenders to hold on to more of their cash.
The restriction on lending is designed to cool growth and limit price rises. However, analysts are divided over whether the action is as effective as using interest rates.
Brazil's central bank holds its next policy meeting on 19 October.
Brazil's inflation rate has spiked to its highest level in more than six years.