The attacks appeared to target the Iranian cultural centre, and an AFP photographer at the scene said the blasts had occurred beyond a security checkpoint at the centre, close to the building.
A security source confirmed that the attack involved two blasts, but could not confirm if the attacks were car or suicide bombings.
Red Cross Secretary General George Kettaneh said three people had been killed and at least 70 wounded, some in serious condition.
Emergency teams carried wounded people away from a charred street strewn with rubble, as local residents armed with fire extinguishers helped firefighters put out blazes.
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The arms of a wounded man hung limply off the sides of a yellow stretcher as he was carried from the scene.
The security official confirmed that the bombs had exploded near the Iranian cultural centre, in the Bir Hassan district of the capital.
Bir Hassan is surrounded by neighbourhoods that are strongholds of the Lebanese Shiite movement Hezbollah and have been targeted in multiple bomb attacks killing civilians.
The group has admitted sending fighters to the neighbouring country to battle alongside Syria's President Bashar al-Assad against an uprising.
Iran's official news agency IRNA too reported that the blast took place near an Iranian cultural centre as well as close to the Beirut offices of IRNA and Iranian television IRIB.
Bir Hassan has been the scene of blasts before, including a powerful double bomb attack against the Iranian embassy there in November that killed 25 people.