An AFP correspondent in the impoverished port city of Tripoli said men, women and children - mostly refugees from Syria but also about 50 Lebanese - were on board the vessel when it got into difficulty.
"Three naval ships, accompanied by another from UNIFIL (the UN mission in Lebanon), arrived at the site... off Selaata and personnel saved some 200 people," the army said on Twitter.
A separate tweet said two people had died.
Earlier, the army said a naval patrol had been dispatched to rescue the vessel packed with people attempting to "illegally leave Lebanese waters".
On Twitter, UNIFIL confirmed it was assisting the Lebanese Navy "in search and rescue operation at sea between Beirut and Tripoli where a boat in distress with a large number of people on board was found."
Dozens of relatives of those rescued streamed into Tripoli port to await their return to shore, AFP's correspondent said.
UK coastguard responds to migrant emergency in English Channel - in pictures
Lebanon is mired in what the World Bank describes as one of the worst economic crises in modern history. The country also hosts more than a million refugees from Syria's civil war.
It was once just a launchpad for foreign migrants, but nearly three years of economic collapse have left Lebanon's own citizens increasingly joining Syrian and Palestinian refugees clamouring to leave by dangerous sea routes.
"We can no longer live in this country - or Syria," said Younes Jomaa, a Syrian originating from Idlib and a brother of one of the surviving migrants.
Migrants cross from Morocco to Spanish enclave of Melilla - in pictures
They are among millions displaced over more than a decade by Syria's war.
"I had planned to go with my brother, but was unable to get enough money together," Mr Jomaa said, adding that his brother had taken on debt to fund his voyage.
Migrant children rescued in French waters - in pictures
In late September around 100 migrants died when their boat sank off the Syrian coast after departing from Lebanon, in one of the deadliest such episodes.
The UN's refugee agency UNHCR has said at least 1,570 individuals, including 186 Lebanese nationals, had embarked or tried to embark on illicit sea journeys from Lebanon between January and November 2021.