"The number of wounded soldiers has risen to five," said the official yesterday, who spoke to AFP on condition of anonymity.
"Six gunmen were injured and six others were arrested."
The clash that initially erupted in the souks (traditional markets) area of Lebanon's second city also extended to other areas.
Tripoli's historic heart is listed by UNESCO as a world heritage site.
Ever since the war in neighbouring Syria broke out in 2011, Tripoli has been the scene of regular fighting between Sunni militants and members of Lebanon's Alawite minority.
Hezbollah has sent thousands of fighters into Syria to support President Bashar al-Assad.
Yesterday's clashes were the first since the outbreak of Syria's war to break out in the souks area, which is traditionally a touristic site.