The incident occurred on Thursday morning when two masked militants on a motorbike opened fire on the officer, identified as Fadi Jbail.
In a separate incident, Lebanese internal security officer was targeted in another attack in the same city, but managed to escape unharmed.
Tripoli, Lebanon’s second largest city, has witnessed deadly fighting between armed men from rival neighborhoods since the outbreak of the conflict in Syria.
Residents of Bab al-Tabbaneh support foreign-backed militants operating against the Syrian government, while the inhabitants of neighboring Jabal Mohsen are loyal to Syrian President Bashar al-Assad.
On Wednesday, at least three people died in renewed fighting between the two neighborhoods.
Nearly 30 people have been killed in similar clashes in Tripoli over the past two weeks.
Meanwhile, Lebanon has been suffering from terrorist attacks carried out by al-Qaeda-linked militant groups, as well as random rocket attacks, which are viewed as a spillover of violence from Syria.
Syria has been plagued by deadly violence since 2011. Some sources say over 140,000 people have been killed and millions displaced due to the foreign-backed militancy.
The Western powers and their regional allies -- especially Qatar, Saudi Arabia and Turkey -- are reportedly supporting the militants operating inside Syria.