Defence Minister Dawoud Rajha, 65, is the most senior government official to be killed in the Syrian civil war as rebels battle to oust President Bashar Assad.
The capital has seen four straight days of clashes pitting government troops against rebels - an unprecedented challenge to government rule in the tightly controlled capital.
Rajha, a former army general, was the most senior Christian government official in Syria. Assad appointed him to the post last year.
His death will resonate with Syria's minority Christian population, who make up about 10 percent of Syria's population and have generally stood by the regime.
Christians say they are particularly vulnerable to the violence sweeping the country of 22 million people, and they are fearful that Syria will become another Iraq, with Christians caught in the crossfire between rival Muslim groups.
Wednesday's attack struck the National Security building in Damascus during a meeting of Cabinet ministers and senior security officials. State-run TV said some of the officials were seriously wounded, and later reported the defence minister killed.
Damascus-based activist Omar al-Dimashki said Republican Guard troops surrounded the nearby al-Shami Hospital where some officials were taken for treatment.
Facing increasingly chaotic violence, the U.N. Security Council was scheduled to vote later on Wednesday on a new resolution aimed at pressuring the Syrian regime to comply with a peace plan.
But Russia remained at loggerheads with the U.S. and its European allies over any mention of sanctions and Chapter 7 of the U.N. charter, which could eventually allow the use of force to end the conflict in Syria.
Besides a government crackdown, rebel fighters are launching increasingly deadly attacks on regime targets, and several massive suicide attacks this year suggest al-Qaida or other extremists are joining the fray.
Activists say more than 17,000 people have been killed since the uprising began in March 2011.
The state-run news agency SANA reported that Wednesday's blast was aimed at the National Security building, a headquarters for one of Syria's intelligence branches and less than 500 meters (yards) from the U.S. Embassy.
Police had cordoned off the area, and journalists were banned from approaching the site.
Earlier on Wednesday, SANA said soldiers were chasing rebels in the Midan neighborhood, causing "great losses among them." The Britain-based Syrian Observatory for Human Rights said army helicopters attacked the neighborhoods of Qaboun and Barzeh.
Diplomacy so far has failed to stop the bloodshed, and there appeared to be little hope that the U.N.'s most powerful body would unite behind a plan.
The key stumbling block is the Western demand for a resolution threatening non-military sanctions and tied to Chapter 7 of the United Nations Charter, which could eventually allow the use of force to end the conflict in Syria.
Russia is adamantly opposed to any mention of sanctions or Chapter 7. After Security Council consultations late Tuesday on a revised draft resolution pushed by Moscow, Russia's deputy U.N. ambassador Alexander Pankin said these remain "red lines."
Russia has said it will veto any Chapter 7 resolution, but council diplomats said there is still a possibility of last-minute negotiations.