The fighting erupted after reports emerged that army troops had shot dead an anti-Syria Sunni cleric when his convoy failed to stop at a checkpoint in north Lebanon on Sunday.
The cleric's killing followed a week of intermittent clashes that left 10 people dead in the northern port city of Tripoli between Sunnis hostile to the Syrian regime and Alawites who support Assad.
The Alawite sect is an offshoot of Shia Islam to which Assad belongs and which has controlled Syrian politics for decades.
The violence in Lebanon has raised fears of a repeat of sectarian unrest in 2008 that pitted Sunnis against Shiites and brought the country close to civil war.
The revolt in Syria has exacerbated a deep split between Lebanon's political parties where the opposition backs those leading the uprising against Assad while a ruling coalition led by the powerful Shiite Hizbollah supports the regime.
The opposition has accused Assad of seeking to sow chaos in Lebanon in order to relieve the pressure on his embattled regime.
Lebanese newspapers on Monday carried ominous headlines warning of civil strife.
"Lebanon boils after sheikh killing" said the front-page headline in The Daily Star.
The English language paper warned in an editorial that the killing of the Muslim cleric on Sunday and other recent incidents had further inflamed tensions linked to the Syria unrest.
"These ingredients create a recipe for the possibility in Lebanon of civil or sectarian strife, the likelihood of which some have been warning about for a while now," it said.
The French language L'Orient-Le-Jour stated in its headline: "Lebanon forcibly dragged into the Syrian storm."
"The destabilisation of Lebanon, with the Syrian crisis as a background, is ongoing," added the daily.
More than 12,000 people, the majority of them civilians, have died in Syria since an anti-regime revolt broke out in March last year, according to the Syrian Observatory for Human Rights.
Syria long held sway in Lebanon politics and had troops stationed in the country for 29 years until it was forced to withdraw them in 2005 following the assassination of ex-premier Rafiq Hariri.
It has denied accusations that it was involved in his killing.