|Daoud Rajiha [photo: BBC]|
The deputy head of the armed forces, President Assad's brother-in-law Assef Shawkat, is also reported to have died.
Other senior officials meeting inside at the time are said to be critically hurt.
The attack comes amid claims of a major rebel offensive on the city.
Syrian officials have downplayed the attacks.
"The Minister of Defence was martyred by the terrorist bombing that targeted the national security building," the TV report said.
Security sources say the suspected bomber worked as a bodyguard for members of President Bashar al-Assad's inner circle.
Gen Rajiha has been defence minister for less than a year, serving previously as chief of staff, and is on a US blacklist for his role in the suppression of dissent.
He is believed to be an Orthodox Christian - a rarity in the Alawite-dominated Syrian military and government.
The attack comes as UN chiefs have been trying to persuade China and Russia to agree tougher measures on Syria, ahead of a Security Council vote on Wednesday on imposing sanctions.
UN-Arab League envoy Kofi Annan held talks with Russian President Vladimir Putin in Moscow, and UN Secretary General Ban Ki-moon met Chinese leader Hu Jintao in Beijing.