That's just slightly up from the single-digit approval ratings Rousseff faced last year.
The new survey by the Ibope polling agency comes at a critical moment for Rousseff, who is fighting impeachment proceedings in Congress over allegations of fiscal mismanagement.
The specter of impeachment looms larger after Brazil's largest party pulled out of Rousseff's governing coalition earlier this week. Without the PMDB party, it will be harder for Rousseff to secure the 172 votes she needs to block the impeachment in the lower house.