The blasts occurred almost simultaneously and struck a Shia community centre and a nearby bakery in the commercial and residential area of Borj al-Barajneh, security sources said.
Interior Minister Nouhad Machnouk said a third suicide bomber had been killed by one of the explosions.
Lebanon arrests three for 'spying for Israel'
The blasts, which were also close to a closely guarded Hezbollah-run hospital, were the first attacks for more than a year in a stronghold of Iran-backed Hezbollah, which has sent fighters to Syria to fight alongside President Bashar al-Assad's forces in the country's civil war.
Medics rushed to treat the wounded after the explosions, which damaged shopfronts and left the street stained with blood and littered with broken glass.
Hezbollah says presence in Syria greater than ever before
The army set up checkpoints at all entrances to the southern suburbs and Hezbollah's own security force was on high alert.
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