"General Ghazi Kanaan, minister of the interior, committed suicide this morning in his office in Damascus," Sana said.
"The relevant authorities are investigating," the agency added.
The suicide comes days before the expected release of a UN report into the assassination of a former Lebanese prime minister Rafiq al-Hariri.
Kanaan, 63, was intelligence chief in Lebanon from the 1980s until 2003, presiding over Syria's control of its neighbouring country.
He reportedly was questioned by UN investigators in the inquiry of al-Hariri's murder.
Aljazeera's correspondent in Syria, Abd al-Hamid Tawfiq, said the Syrian cabinet announced his death on Wednesday.
The Syrian news agency's statement merely said investigations are under way into the circumstances of the suicide.
Tawfiq said quoting Syrian sources that Kanaan committed suicide at 11am (Damascus local time) on Wednesday. His body has been transferred to al-Shami hospital in Damascus.
UN investigator Mehlis had taken
testimonies from Syrian officials
The Syrian government has started investigations into the reasons and circumstances of Kanaan's death, Tawfiq added.
It was not clear whether he shot himself.
Shortly before his death, Kanaan gave an interview to Sawt Libnan (Voice of Lebanon] radio station, at the end of which he said: "I believe this is the last announcement I can make."
He told the interviewer: "What is being reported about secret links exists only in the minds of those who spread such reports, to serve their political interests and malicious objectives.
"I hope they will be objective and fear God in what they say."
In the radio interview, Kanaan defended the presence of Syrian troops in Lebanon, saying they had "done their utmost to preserve the unity of Lebanon" during their 29-year deployment.
The deployment came to an end in April amid local and international outrage over al-Hariri's killing.
Kanaan said 'we have served the
interests of Lebanon with dignity'
Kanaan also accused the media of damaging relations between the two countries.
He said reports since al-Hariri's 14 February assassination in a massive bomb blast on the Beirut seafront, had wronged both himself and the former Lebanese premier.
The killing was widely blamed on Syria, which has repeatedly denied any involvement.
"We have affection and mutual respect for Lebanon ... We have served the interests of Lebanon with dignity," Kanaan said, denying reports in the Lebanese media that he showed the UN investigators cheques paid to him by al-Hariri.
On 20 July, Kanaan was quoted in the Beirut daily As-Safir as saying he had no information on the murder, stressing that military intelligence was only in charge of security for Syrian troops and coordination with Lebanese authorities.
Tawfiq said report of the Syrian minister's suicide had caught both domestic and foreign analysts by surprise. So far no comment or analysis has been forthcoming from Syrian official sources.
Kanaan was among those whose testimonies were taken by UN investigator Mehlis, but no official or unofficial statements have been issued linking the suicide to the investigation.
"What is being reported about [secret] links exists only in the minds of those who spread such reports, to serve their political interests and malicious objectives"
Ghazi Kanaan in his last interview before death
Mehlis interviewed Kanaan two weeks ago during his last visit to Damascus, the correspondent added.
Kanaan was the head of Syrian security and military intelligence in Lebanon for several years until 2003. In that capacity, he worked directly with different Lebanese groups.
Kanaan becomes the first Syrian official to commit suicide since Syrian prime minister Mahmud al-Zubi took his own life in the late 1990s, Tawfiq said.