The failure of parliament to elect a new president reflects a profound political crisis linked to the war in neighbouring Syria.
"Yesterday Prime Minister (Tammam) Salam gave a message during the parliamentary session that we would not celebrate Independence Day this year... because of the presidential vacuum," minister Ramzi Jreij told AFP.
Lebanon was due to mark the 71st anniversary of its independence from France on Saturday with a parade involving all the country's security forces.
The cancellation is the first since the end of the civil war, and comes amid a stalemate over the election of a successor to president Michel Sleiman, who stepped down in May.
"For the first time, the Independence Day celebrations are being cancelled, because of the presidential vacuum," a military source confirmed.
The day is usually marked with a speech to the nation by the president on the eve of the holiday and a military parade on the day itself in Beirut, attended by the country's political leadership.
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Another military source said the decision to cancel the celebrations was also influenced by an ongoing crisis involving the kidnapping of 27 security forces by jihadists.
The men -- soldiers and police -- have been held since August, when jihadists from the conflict in Syria briefly overran the town on Arsal, on the Lebanese border.
Three hostages have already been killed by their captors, and the country has been on edge for months over the fate of the remaining 27.
Lebanon is deeply divided over the war in Syria.
Powerful Shiite movement Hezbollah has deployed thousands of troops in Syria to support President Bashar al-Assad's regime.
Most of the country's Sunnis support Syria's anti-Assad revolt.
Lebanon was dominated politically and militarily by Damascus until 2005. Syria continues to exert a strong influence over Lebanese politics through its allies.