Ban said the spillover of the 2 1/2-year conflict has caused more than 800,000 Syrians to flee to Lebanon, straining the country's finances and increasing social pressures.
In a report to the UN Security Council circulated Wednesday, he condemned the shelling, shootings into Lebanon and called on all parties to respect the border.
The Lebanese Armed Forces also reported "continued smuggling of weapons across the Lebanese-Syrian border," Ban said.
The secretary-general said the Syrian conflict was a contributing factor for two terrorist attacks in the southern suburbs of Beirut in July and August and simultaneous car bombings in Tripoli later in August.
The deepening unrest in Lebanon is a troubling sign for a country that has gone through its own 15-year civil war and has an explosive sectarian mix as well as deep divisions between pro- and anti-Syria factions, many of them armed.
In May, Lebanon's parliament extended its mandate by a year and a half by skipping scheduled elections largely because of the instability in the country. Politicians also have been unable to form a new government since outgoing premier Najib Mikati resigned in March.
Ban urged all parties to engage with Prime Minister-designate Tammam Salam to form a new government to address the crises impact on Lebanon.
He also appealed to UN members to step up contributions to an appeal for over $1.6 billion to address refugee needs in Lebanon through the end of 2013.