The officials say the man, identified as Mark Eddie Maximus, was arrested by military intelligence in the northern city of Tripoli over the weekend.
One official speaking to The Associated Press today says authorities had been pursuing Maximus for a while on suspicion of funding a terrorist organization.
He declined to elaborate and spoke on condition of anonymity in line with regulations.
A local newspaper said the man was suspected of ties to the Islamic State group.
The Lebanese army has been fighting the Islamic State group and al-Qaida's Syrian branch, the Nusra Front, in border areas close to Syria.