The police believe that the man himself caused the explosions, and are investigating the incident as a terrorist crime.
The court was evacuated after two powerful explosions around 19:30 local time. The first explosion came from a car on the square outside the court. The second, which also killed the man, occurred near the entrance as the man tried to enter the building, according to Vice Governor Celina Leão.
Federal police describe the explosions as "attacks" and state that they are investigating the incident.
The police cordoned off the area around the court and the nearby presidential palace and congress.
Brazil's President Luiz Inácio Lula da Silva was not in the presidential palace at the time of the explosion, according to a spokesperson for his staff.
