A rocket hit the seventh floor of the AK building, while a bomb was thrown at the ministry, local media say.
Police are said to have made two arrests but no group has said it carried out the attacks.
Kurdish rebels, left-wing groups and Islamist militants have previously bombed targets in Turkey.
The latest blasts follow a police crackdown on a banned Marxist group.
They also come amid reports of a deal between the government and jailed Kurdish rebel leader Abdullah Ocalan.