It said the blast, which occurred at around 21:45 (1845 GMT) in a courtyard, shattered windows in the ministry complex and surrounding buildings and damaged cars parked in the street.
The complex is used as an operations centre for the supply of oil to the Turkish army as well as to NATO, the semi-official Anatolia news agency said.
State-run Anatolian news agency quoted police as saying the explosion was not due to a bomb.
A security camera exploded at a building used by the Turkish Defence Ministry, Anatolian quoted police chief Ercument Yilmaz said.
Witnesses at the scene told Reuters a large number of police had cordoned off the area.
Anatolian quoted witness Ahmet Sener as saying: “I saw metal pieces near the site of the explosion. I then noticed another package, prepared like a gift package, and alerted police.”
A bomb squad also detonated a suspicious package at the site after the initial blast according to CNN Turk.
But it came amid heightened tensions in Turkey as NATO leaders met at a summit in Istanbul.
Turkey, fearing terror attacks, has enacted massive security measures for the summit, calling on duty more than 25,000 police officers, as well as armed forces at land and at sea backed by AWACS early warning aircraft patrolling the skies of the city.
On Thursday, a bomb explosion on a bus in Istanbul killed four people, including the bomber, and left 21 others wounded.
Authorities blamed left-wing armed dissidents for the attack.