The attacker fled after firing three volleys of automatic fire and then apparently committed suicide.
Police said the man’s body was found less than a kilometre away.
Prime Minister Andrej Plenkovic was not in the building at the time of the attack, minutes after 8 a.m. (0600 GMT), a government spokesman said. He arrived within an hour.
The wounded policeman underwent surgery and was in stable condition, according to police.
The motive of the attack was not immediately clear.(dpa/NAN)