Of the military staff ordered detained, three are officers, two are non-commissioned officers and six are soldiers.
Lebanese troops opened fire to break up demonstrators who burned tyres and blocked roads in protest over power cuts in a Beirut suburb on January 27.
Around 30 protesters were also wounded in the incident, which increased tension in a country split by a deep political crisis.
Seven supporters of Hezbollah and Amal, both Shia Muslim parties, were killed in Sunday's street violence.
Ali Ammar, a Hezbollah deputy, accused the army of firing indiscriminately at the protesters and said that the military was being used as a pawn by the coalition.
General Michel Suleiman, Lebanon's army chief, had been under pressure to identify those behind the violence.
Hezbollah had earlier said the army mishandled the protest and demanded that those responsible for the deaths be punished swiftly.
There are fears that the incident could tarnish the army's reputation as the only institution capable of keeping the peace in Lebanon.
Despite the consensus between the majority parliamentary bloc and the opposition to support General Suleiman as Lebanon's next president, differences over the shape of a future government have held up his confirmation as head of state.
Lebanon without a president since November, when Emile Lahoud stepped down.
Also on Saturday, the army said two Lebanese soldiers were wounded in a shooting attack in the same area late on Friday.