"Work is underway to resolve the issue of Lebanese citizens being prevented from entering Syria," Bassam Mawlawi told AFP.
He said Lebanon's General Security agency was in touch with "the Syrian side" to resolve the issue.
The developments appeared to be the first instance of friction between the two neighbours, who share a fraught history, since Islamist-led rebels toppled longtime Syrian leader Bashar al-Assad last month.
Lebanese nationals had previously been allowed into Syria without a visa, using just their passport or ID.
But a Lebanese General Security official told AFP on Friday that they were "surprised to see the border had been closed" to Lebanese citizens "from the Syrian side".
The official, who like other sources spoke on condition of anonymity to discuss sensitive matters, said that no new border measures had been communicated to them yet.
A security source at Masnaa, the main land border crossing between the two countries, said Syrian authorities had implemented "new procedures" since the previous night, only allowing in Lebanese with residency permits or official permission.
Lebanon had imposed similar rules on Syrians entering the country after civil war erupted there more than a decade ago.
The Lebanese army said in a statement on X that its soldiers and armed Syrians had clashed at the border after the armed forces tried to "close an illegal crossing".
The violence left five soldiers wounded, it said in statements.
Lebanon's eastern border is porous and known for smuggling. It was unclear who the armed Syrians were.
"Syrians attempted to open the crossing using a bulldozer, so army personnel fired warning shots into the air. The Syrians opened fire on army personnel, injuring one of them and provoking a clash," the army said.
Later, renewed clashes injured four more soldiers.
Last month, Syria's new leader Ahmed al-Sharaa told visiting Lebanese Druze leaders that his country would not negatively interfere in Lebanon and would respect its sovereignty.
For three decades, Syria was a dominant military and political force in Lebanon after intervening in its 1975-1990 civil war.
Syria eventually withdrew its troops in 2005 under international pressure after the assassination of Lebanese ex-prime minister Rafic Hariri.
