“On Thursday, a 13-year-old child was shot dead by a sniper taking aim into his family home” in a neighborhood the majority of whose residents are Alawite, the same community to which Syria's President Bashar al-Assad belongs, the official said.
Earlier in the day, three others were killed in the Alawite district of Jabal Mohsen and the Sunni Muslim district of Bab al-Tebbaneh, the official said.
Another 20 people were wounded on Thursday, including a Lebanese soldier, he added.
For three days, Tripoli has been rocked by sectarian violence linked to the nearly 21-month uprising in Syria.
Five people were gunned down on Wednesday and another two the previous day.
The violence has pitted Sunni districts against neighboring areas populated by Alawites, and officials say the snipers come from both camps.
On Thursday, troops patrolled the restive areas and were responding to the gunfire, but snipers held their positions and continued to shoot, an AFP correspondent on the scene reported.
Lebanon is deeply divided over Syria. The Shiite movement Hezbollah, its allies and supporters bitterly oppose the revolt, and the Sunni-led March 14 movement backs it.
The country was dominated politically and militarily by Damascus for nearly 30 years, until the 2005 assassination of former premier Rafiq Hariri prompted international outrage and forced a Syrian pullout.
Near-daily clashes in border areas inside Syria pit Shiite residents who support Hezbollah against anti-Assad rebels, residents and activists say.