No one has claimed the attack, but an audio recording posted on YouTube by a Sunni militant group said there would be more "strikes" if the Shiite movement does not pull out of Syria.
The explosion happened around midnight (0230 IST Tuesday) near an army checkpoint and cafe where football fans were watching a World Cup match.
An army statement said a suicide attacker driving a white Mercedes "blew himself up at an army checkpoint at the Tayuneh roundabout (in southern Beirut), wounding several civilians."
Yesterday, the General Security agency confirmed in a statement that Abdel Karim Hodroj, a 20-year-old inspector, had been killed, after carrying out DNA tests on his remains.
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"The martyr Hodroj paid with his life for the mission he was entrusted with, in the national war against terror," said the agency.
A security source had earlier told AFP that Hodroj and his colleague Ali Jaber, who was wounded, "were passing through the area ... They felt a vehicle that was going against the traffic flow was suspicious.
"The vehicle stopped in the middle of the road, and a man got out. (Hodroj and his colleague) stopped him and questioned him. The man said his car key was broken, and he couldn't drive any more," the source said.
"Hodroj remained with the suicide attacker to ensure he wouldn't get away," the security source said.
Jaber was 30 metres away when the explosion happened.
The General Security statement added: "The martyr sacrificed himself to save a significant number of soldiers and civilians who would have fallen victim to the terrorist's plan."
The bombing came three days after a suicide attack in eastern Lebanon killed one person and wounded 30.
Southern Beirut, a stronghold of Lebanon's Shiite movement Hezbollah, has been targeted by attacks for months.