Two other people were reportedly wounded in the violence. The shots were fired after followers of the Future bloc of Saad al-Hariri, the prime minister-designate, clashed with supporters of Amal, which is led by Nabih Berri, the parliamentary speaker.
An army spokesman said that Sunday's fighting had lasted between two and three hours, but soldiers had now been deployed to keep calm in the area.
"Orders have been given to [the army] to open fire on any armed person appearing on the streets and it will not tolerate any breach of security," a statement from the army leadership said.
The fighting came just a day after Hariri was named as prime minister-designate with the support of MPs from Amal, part of the opposition bloc which also includes the Hezbollah.
Amal and Hezbollah are regarded as political representatives of Lebanon's Shia Muslim community. The Future bloc, on the other hand, draws much of its support from the country's Sunni Muslim.
After accepting the invitation to form a government, Hariri has pledged to work with the opposition "to have a harmonious government that will respresent the interests of all Lebanese people".
Hariri, whose bloc retained the parliamentary majority after defeating the opposition alliance in general elections on June 7, is expected to begin negotiations in an attempt to pick a cabinet on Monday.
Heavy clashes previously erupted between the two factions in May 2008, with Hezbollah, backed by Amal, seizing control of some predominantly Sunni Muslim parts of west Beirut.
More than 100 people were killed in the violence.
An uneasy peace was restored after the two sides agreed to form a government of national unity with veto power for the opposition bloc.