A young girl was killed and three soldiers wounded by the blasts. Four others were hurt when an attacker threw a hand grenade, the army said.
It happened during an operation to search for militants and weapons in an area near the town of Arsal.
Arsal has often seen violence between troops and Sunni jihadists.
In the raid on Friday, four suicide bombers struck in one refugee camp, and a fifth struck in another camp, the army said.
Some 350 people were detained, including officials from the Islamic State (IS) group, Reuters news agency quoted a security source as saying.
The area is home to tens of thousands of refugees from the war in Syria. The influx has heightened sectarian tensions inside Lebanon since the conflict began in 2011.
A Sunni enclave surrounded by Shia villages, Arsal was the scene of an attack in 2014, when more than two dozen Lebanese security force members were seized by militants from al-Qaeda and IS who had crossed the border from Syria.
Sixteen have since been released and four killed by their captors.
Security forces say members of IS and jihadist group Jabhat Fateh al-Sham have a strong presence in and around the town.
The groups are active in hills overlooking Arsal, where they were pushed back in an offensive by Syrian government and allied Shia Hezbollah forces in mid-2015.
Five militants have blown themselves up during a raid by Lebanese troops on refugee camps near the Syrian border, Lebanon's army said.