Four of the seven wounded were hospitalised, while the rest were given first aid at the scene, medical sources said.
The Lebanese attorney-general has called for an inquiry into the incident, Aljazeera reported.
The scuffle on Tuesday broke out after the relatives tried to hand over a statement to pro-Syrian MP Adnan Arakji in his car as he drove towards the parliament building.
One of Arakji's guards opened fire and then hit a civilian with his pistol, reported Aljazeera correspondent Ghassan bin Jiddo.
"We were giving the statement to every deputy and there were no problems until the car of MP Adnan Arakji forced its way through the crowd," said one of the relatives, Violette Nassif.
Lebanese security forces were
deployed in large numbers
"The crowd started hitting the car. Bodyguards then stepped out of the car, fired into the air and beat some of the relatives before the army intervened," she said.
The clashes spread between relatives of the prisoners and Lebanese security and army forces, who had been heavily deployed in Riyad al-Sulh square and at the gates of the Parliament, reported the correspondent.
Protesters first chanted anti-Syria slogans and later turned their ire on local security forces and pro-Syrian Lebanese, he reported.
Nassif said the relatives' statement called on MPs to put pressure on the new Lebanese government to help resolve the missing persons issue, as Syria wound up its 29-year military presence in Lebanon on Tuesday.
On 11 April, dozens of relatives of about 280 Lebanese presumed missing or imprisoned in Syria started an open-ended hunger strike in front of the headquarters of the United Nations in downtown Beirut.
"The crowd started hitting the car. Bodyguards then stepped out of the car, fired into the air and beat some of the relatives before the army intervened"
protester Violette Nassif
In December 2000, Syria released 54 Lebanese prisoners from its jails.
Damascus then considered the issue closed, but the Lebanese government has opened an inquiry under pressure from relatives and rights groups. The results of the inquiry have not been released.