Officials first found a suspicious package in the grounds of the centre and it exploded after one of the them threw it into an empty building around 7:45 am (0445 GMT).
The blast shattered windows but caused no injuries, reported Anatolia news agency.
Officials at the compound, an education centre for trainee judges and state prosecutors, subsequently discovered a second package in the grounds, which exploded as police began to investigate.
The injured officers were taken to hospital and police were conducting an investigation at the scene.
Leftist rebels and Kurdish guerrillas have been involved in a number of bombings in Turkey in recent years. In September 2001, two police officers, an Australian tourist and the suicide bomber were killed in a leftist attack in Istanbul.