The National News Agency says the explosion struck an army vehicle in the Arsal region and that the wounds sustained by the troops were minor.
The blast was followed by the soldiers opening fire with heavy weapons at militant positions nearby.
Violence from neighbouring Syria's civil war has spilled across the border into Lebanon in the past. Islamic State and al-Qaida militants briefly seized the Lebanese border town of Arsal in 2014, before Lebanese security forces pushed them back to the frontier.
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